Practice Test

1) A S.H.M. oscillator has period of 0.1 sec. and amplitude of 0.2 m. The maximum velocity is given by:

2) If a hole is drilled along the diameter of the earth and a stone is dropped into it. The stone:

3) Total energy of the particle executing S.H.M. is proportional to:

4) A pendulum suspended to the ceiling of a train has a period T when the train is at rest. If the train is accelerated uniformly the period will:

5) A pendulum is first vibrated on the surface of earth. Its period is T. It is then taken to the surface of moon where acceleration due to gravity is 1/6th of that on earth. Its period will be:

6) A simple pendulum is made of a hollow spherical bob full of mercury and suspended by a thin string. If the mercury begins to leak from the small hole at its bottom, then its time period:

7) A simple pendulum has a bob which is given negative charge. It is then allowed to oscillate just above a uniformly positively charged plate, its period:

8) The potential energy of particle executing S.H.M. with amplitude A is maximum when displacement is:

9) The kinetic energy of particle executing S.H.M. with amplitude A is maximum when displacement is:

10) If the lift moves up with uniform speed, then period is:

11) The work done by the string of a simple pendulum during one complete vibration is:

12) A particle is executing S.H.M. with the length of its path as 8 cm. At what displacement from the mean position half the energy is kinetic and half is potential?

13) An object attached to a light spring oscillates in S.H.M. on a horizontal smooth surface. The ratio of maximum P.E. to maximum K.E. is:

14) The time period of a second's pendulum is:

15) A boy swinging on a swing in sitting position suddenly stands up. The period of swing will then be:

16) If the two springs are suspended in parallel and the system is collectively loaded with mass 'm', then period is:

17) A particle is executing S.H.M. with period 12 sec. The time it takes in traversing a distance equal to half its amplitude is:

18) If the length of a simple pendulum is increased by 2% then time period (approx):

19) If condenser of capacitance 'C' is discharged through inductance 'L' the charge oscillates harmonically with angular frequency:

20) The length of the seconds pendulum is increased by 0.1%. The clock:

21) Two bodies A and B of mass 1 kg and 2 kg are soldered to two ends of vertical spring of force constant 400 N/m. A being at the upper end and B resting on a table. A is now compressed and then released. The freq. of oscillation is:

22) In S.H.M. the acceleration of the particle is zero when the velocity is:

23) A particle executes S.H.M. with amplitude 25 cm and period 3 s. What is the minimum time required for it to move between two points 12.5 cm on either side of the mean position?

24) A spring balance has a scale reading from 0 to 50 kg. The length of the scale is 20 cm. A body suspended to the spring of the balance when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body?

25) A particle executes S.H.M. with amplitude 2 cm. At a distance 1 cm from the mean position of magnitudes of the velocity and acceleration are equal. The time period of oscillation is:

26) A mass of 1 kg is suspended form a spring and has a time period T on the surface of earth. The period at the centre of earth is:

27) Two pendulum starts swinging together when their lengths are 1.44 m and 1.0. After how many vibrations they will again start swinging together?

28) A particle executes S.H.M. Its amplitude is A and period is T. At a time its speed is half the maximum speed. What is the displacement?

29) A second's pendulum is placed in a space laboratory orbiting round the earth at a height of 3 R, where R is the radius of earth. The time period of the pendulum is:

30) A particle executes S.H.M. with amplitude 2 cm. At extreme position the force is 4 N. The force acting on it at a position mid-way between the mean and extreme is:

31) The average acceleration in one time period in a S;H.M. is:

32) If a watch with a wound spring is taken into the moon, it:

33) A block of mass m rests on a platform. The platform is given up and down S.H.M. with an amplitude d. What can be the maximum frequency so that the block never leaves the platform?

34) In a certain engine, a piston undergoes vertical S.H.M. with amplitude 7 cm. A washer rests on top of piston. As the motor is slowly speeded up, at what frequency will the washer no longer stay in contact with the piston?

35) A particle under the action of an S.H.M. has a period 3 sec and under the effect of another it has a period 4 sec, what will be its period under the combined action of both the simple harmonic motions in the same direction?

36) If the potential energy of a harmonic oscillator in its resting position is 500 erg and total energy is 1500 erg when the amplitude is 5 cm what is the force constant if its mass is 200 gm?

37) Two pendula of lengths 121 cm and 100 cm start vibrating. At some instant the two are in the mean position in the same phase. After how many vibrations of the shorter pendulum the two will be in phase in the mean position?

38) A clock A is based on oscillations of spring and a clock B is based on pendulum motion. Both clocks run at the same rate on earth. On a planet having the same density as earth but twice the radius:

39) If potential energy of a harmonic oscillator in its resting position is 15 joule and the average K.E. is 5 joule, then the total energy at any instant is:

40) A body executes S.H.M. with an amplitude A. At what displacement from the mean position is the potential energy of the body is one-fourth of its total energy?

41) A simple pendulum is executing simple harmonic motion with a time period T. If the length of pendulum is increased by 21%, the % increase in the time period of the pendulum of increased length is:

42) Two particles P and Q start from the origin and execute S.H.M. along x-axis with same amplitudes but with periods 3 sec. and 6 sec. The ratio of the velocities of P and Q when they meet is:

43) Two springs of spring constants 1500 N/m and 3000 N/m respectively are stretched with the same force. They will have potential energy in the ratio:

44) A spring 40 mm long is stretched by the application of a force. If 10 N force is required to stretch the spring through 1 mm, then work done in stretching the spring through 40 mm is:

45) A cubical body (side 0.1 metre and mass 0.002 kilogram) is floating in water. It is pressed and released by which it vibrates. The time period of vibration will be:

46) A sphere of 200 g is tied from one end of a 130 cm long rope, whose second end is tied from the ceiling. Sphere is moving in a horizontal circle of 50 cm. The time period of conical pendulum will be:

47) One-fourth length of a spring with force constant 'k' is cut away. The force constant of the remaining part is:

48) A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total energy (T.E.) are measured as a function of displacement X. Which of the following statements is true?

49) The total energy of a particle, executing S.H.M. is:

50) The maximum velocity of a particle executing simple harmonic motion with an amplitude 7 mm is 4.4 m/s . The period of oscillation is:

51) Starting from origin a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy be 75% of the total energy?

52) A hollow sphere filled with water forms the bob of a simple pendulum. A small hole at the bottom of the bob allows the water to oscillation and its period of oscillation is measured. The time period will:

53) In a simple pendulum, if K.E. is one-fourth of total energy then displacement (x) is related to amplitude 'A', as:

54) When the displacement is half the amplitude the ratio of potential energy to the total energy is:

55) Two simple pendulums of length 0.5 m and 2.0 m respectively are given small linear displacement in one direction at the same time. They will again be in the pendulum of shorter length has completed oscillations:

56) In a sinusoidal wave, the time required for a particular point to move to maximum displacement is 0.17 sec. The frequency of the wave is:

57) A child is sitting on a swing. Its minimum and maximum heights from the ground are 0.75 m and 2 m respectively. Its maximum speed will be:

58) The total energy of a particle performing S.H.M. depends on:

59) The ratio of kinetic energy of mean position to the potential energy when the displacement is half of the amplitude is:

60) A lift is ascending with an acceleration equal to g/3. What will be time period of the simple pendulum suspended from its ceiling if its time period in stationary lift is T?

61) A pendulum suspended from ceiling of a train has a time period T, when the train is at rest. When the train is accelerating with uniform acceleration 'a', the period of oscillation will

62) Period of oscillation of mass attached to a spring and performing S.H.M. is T. The spring is now cut into four equal pieces and the same mass attached to one piece. Now the period of its simple harmonic oscillation is:

63) The P.E. of a simple harmonic oscillator, when the particle is half way to its end point is:

64) In case of a forced vibrations, the resonance wave becomes very sharp when the:

65) A particle performs S.H.M. with a period of 2 seconds. The time taken by it to cover a displacement equal to half of its amplitude from the mean position is:

66) The equation of motion of simple harmonic oscillation is:

67) The time period of a mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts; then the new time period will be:

68) Pendulum after some time becomes slow in motion and finally slopes due to:

69) The period of oscillation of a simple pendulum is T in a stationary lift. It the lift move upwards with acceleration of 8g the time period will:

70) A particle executing simple harmonic motion of amplitude 5 cm has maximum speed 31.4 cm/s. The frequency of its oscillation is:

71) Which of the following functions represents a simple harmonic oscillations?

72) Which of the following is not characteristics of S.H. oscillations?

73) The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is:

74) The period of oscillation of a mass M suspended from a spring of negligible mass is T. If along with it another mass M is also suspended, the period of oscillation will now be:

75) A large horizontal surface moves up and down in simple harmonic motion with an amplitude of 1 cm. If a mass of 10 kg (which is placed on this surface) is to remain continuously in contact with it, the frequency of S.H.m. should not exceed:

76) A particle is vibrating in simple harmonic motion with an amplitude of 4 cm. At what displacement from the equilibrium position is its energy half potential and half kinetic?

77) A heavy brass sphere is hung from a spiral and it executes vertical vibrations with period T. The sphere is now immersed in a non-viscous liquid with a density 1/10th of that of brass. When set into vertical vibrations with the sphere remaining inside liquid all the time, the time period will be:

78) A hollow metal sphere is filled with water and is hung by a long thread. It is made to oscillate. If water slowly flows through a small hole in the bottom, how will the period of oscillation be affected?

79) On an average a human heart is found to beat 75 times in a minute. Its time-period is

80) The potential energy of the block at x = 5 cm is

81) The length of a seconds pendulum, which ticks seconds is

82) Which of the following relationships between the acceleration a and the displacement x of a particle involve SHM?

83) A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. The weight of the body is

84) The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, its maximum speed is

85) The time period of a simple pendulum mounted in a cabin that is freely falling under gravity is

86) Obtain the SHM motion of the x-projection of the radius vector of the rotating particle P

87) The maximum speed of the mass is

88) Let us take the position of mass when the spring is unstretched as x = 0, and the direction from left to right as the position direction of x-axis. Give x as function of time t for the oscillating mass if at the moment we start the stopwatch (t = 0), the mass is at the maximum compressed position.

89) A pendulum clock keeping correct time is taken to high altitudes.

90) The velocity and acceleration of a particle executing SHM have a steady phase relationship. The acceleration leads velocity in phase by

91) The tension in the string of a simple pendulum is

92) A hollow metallic sphere is filled with water and hung by a long thread. A small hole is drilled at the bottom through which water slowly flows out. Now, the sphere is made to oscillate. The period of oscillation of sphere

93) A simple pendulum is made of body which is a hollow sphere containing mercury suspended by means of a wire. If a little mercury is drained off, the period of the pendulum will

94) What fraction of the total energy is kinetic when the displacement is one-half of the amplitude?

95) Which of the following quantities are always positive in a simple harmonic motion? (Letters have usual meanings)

96) The equation of a SHM of amplitude a and angular frequency omega in which all distance are measured from one extreme position and time is taken to be zero at the other extreme position is

97) Time period of SHM is

98) Magnitude of acceleration is

99) angular velocity of particle is

100) A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is T. If the spring is divided in two equal parts and one part is used to continue the simple harmonic motion, the time period will

101) A particle executes an undamped SHM of time period T. Then the time period with which the potential energy changes is

102) Two particles execute SHM of same amplitude and frequency along the same straight line. They pass one another when going in opposite directions, each time their displacement is half of their amplitude. The phase difference between them is

103) A 1 kg block is executing simple harmonic motion of amplitude 0.1 m on a smooth horizontal surface under the restoring force of a spring of spring constant 100 N//m. A block of mass 3 kg is gently placed on it at the instant it passes through the mean position. Assuming that the two blocks move together, the amplitude of the motion is

104) The amplitude and the periodic time of a S.H.M. are 5 cm and 6 sec respectively. At a distance of 2.5 cm away from the mean position, the phase will be

105) The phase (at a time t) of a particle in simple harmonic motion tells

106) A particle is moving with constant angular velocity along the circumference of a circle. Which of the following statements is true

107) Which of the following equation does not represent a simple harmonic motion

108) A particle executing S.H.M. of amplitude 4 cm and T = 4 sec. The time taken by it to move from positive extreme position to half the amplitude is

109) A particle is moving in a circle with uniform speed. Its motion is

110) The periodic time of a body executing simple harmonic motion is 3 sec. After how much interval from time t = 0, its displacement will be half of its amplitude

111) A body is executing simple harmonic motion with an angular frequency 2 rad/s. The velocity of the body at 20 mm displacement, when the amplitude of motion is 60 mm, is

112) A body of mass 5 gm is executing S.H.M. about a point with amplitude 10 cm. Its maximum velocity is 100 cm/sec. Its velocity will be 50 cm/sec at a distance

113) A particle is executing S.H.M. If its amplitude is 2 m and periodic time 2 seconds, then the maximum velocity of the particle will be

114) If a simple pendulum oscillates with an amplitude of 50 mm and time period of 2 sec, then its maximum velocity is

115) A particle executes simple harmonic motion with an amplitude of 4 cm. At the mean position the velocity of the particle is 10 cm/s. The distance of the particle from the mean position when its speed becomes 5 cm/s is

116) Two particles P and Q start from origin and execute Simple Harmonic Motion along X-axis with same amplitude but with periods 3 seconds and 6 seconds respectively. The ratio of the velocities of P and Q when they meet is

117) The velocity of a particle in simple harmonic motion at displacement y from mean position is

118) Which of the following is a necessary and sufficient condition for S.H.M.?

119) If a hole is bored along the diameter of the earth and a stone is dropped into hole

120) The amplitude of a particle executing S.H.M. with frequency of 60 Hz is 0.01 m. The maximum value of the acceleration of the particle is

121) A small body of mass 0.10 kg is executing S.H.M. of amplitude 1.0 m and period 0.20 sec. The maximum force acting on it is

122) For a particle executing simple harmonic motion, which of the following statements is not correct

123) A particle moving along the x-axis executes simple harmonic motion, then the force acting on it is given by Where A and K are positive constants

124) A body is vibrating in simple harmonic motion with an amplitude of 0.06 m and frequency of 15 Hz. The velocity and acceleration of body is

125) A particle is executing simple harmonic motion with an amplitude of 0.02 meter and frequency 50 Hz. The maximum acceleration of the particle is

126) A particle executes simple harmonic motion along a straight line with an amplitude A. The potential energy is maximum when the displacement is

127) A particle is vibrating in a simple harmonic motion with an amplitude of 4 cm. At what displacement from the equilibrium position, is its energy half potential and half kinetic

128) The potential energy of a particle with displacement X is U(X). The motion is simple harmonic, when (K is a positive constant)

129) The total energy of the body executing S.H.M. is E. Then the kinetic energy when the displacement is half of the amplitude, is

130) The P.E. of a particle executing SHM at a distance x from its equilibrium position is

131) A vertical mass-spring system executes simple harmonic oscillations with a period of 2 s. A quantity of this system which exhibits simple harmonic variation with a period of 1 s is

132) For any S.H.M., amplitude is 6 cm. If instantaneous potential energy is half the total energy then distance of particle from its mean position is

133) A particle starts simple harmonic motion from the mean position. Its amplitude is a and total energy E. At one instant its kinetic energy is Its displacement at that instant is

134) A particle executes simple harmonic motion with a frequency f . The frequency with which its kinetic energy oscillates is

135) A particle moves such that its acceleration a is given by a = - b x, where x is the displacement from equilibrium position and b is a constant. The period of oscillation is

136) A tunnel has been dug through the centre of the earth and a ball is released in it. It will reach the other end of the tunnel after

137) The kinetic energy of a particle executing S.H.M. is 16 J when it is in its mean position. If the amplitude of oscillations is 25 cm and the mass of the particle is 5.12 kg, the time period of its oscillation is

138) To make the frequency double of an oscillator, we have to

139) What is constant in S.H.M.

140) Mark the wrong statement

141) A particle executes SHM in a line 4 cm long. Its velocity when passing through the centre of line is 12 cm/s. The period will be

142) The period of a simple pendulum is doubled, when

143) A pendulum suspended from the ceiling of a train has a period T, when the train is at rest. When the train is accelerating with a uniform acceleration a, the period of oscillation will

144) The mass and diameter of a planet are twice those of earth. The period of oscillation of pendulum on this planet will be (If it is a second's pendulum on earth)

145) Which of the following statements is not true? In the case of a simple pendulum for small amplitudes the period of oscillation is

146) The time period of a second's pendulum is 2 sec. The spherical bob which is empty from inside has a mass of 50 gm. This is now replaced by another solid bob of same radius but having different mass of 100 gm. The new time period will be

147) The length of the second pendulum on the surface of earth is 1 m. The length of seconds pendulum on the surface of moon, where g is 1/6th value of g on the surface of earth, is

148) The period of simple pendulum is measured as T in a stationary lift. If the lift moves upwards with an acceleration of 5 g, the period will be

149) The length of a simple pendulum is increased by 1%. Its time period will

150) Identify correct statement among the following

151) A simple pendulum executing S.H.M. is falling freely along with the support. Then

152) If the metal bob of a simple pendulum is replaced by a wooden bob, then its time period will

153) In a simple pendulum, the period of oscillation T is related to length of the pendulum l as

154) If the length of simple pendulum is increased by 300%, then the time period will be increased by

155) The length of a seconds pendulum is

156) The time period of a simple pendulum in a lift descending with constant acceleration g is

157) A chimpanzee swinging on a swing in a sitting position, stands up suddenly, the time period will

158) In a seconds pendulum, mass of bob is 30 gm. If it is replaced by 90 gm mass. Then its time period will

159) The time period of a simple pendulum when it is made to oscillate on the surface of moon

160) A simple pendulum, suspended from the ceiling of a stationary van, has time period T. If the van starts moving with a uniform velocity the period of the pendulum will be

161) If the length of the simple pendulum is increased by 44%, then what is the change in time period of pendulum

162) To show that a simple pendulum executes simple harmonic motion, it is necessary to assume that

163) The height of a swing changes during its motion from 0.1 m to 2.5 m. The minimum velocity of a boy who swings in this swing is

164) A simple pendulum hangs from the ceiling of a car. If the car accelerates with a uniform acceleration, the frequency of the simple pendulum will

165) The ratio of frequencies of two pendulums are 2 : 3, then their length are in ratio

166) Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is 7 : 8, then the ratio of lengths of the two pendulums will be

167) If the length of a pendulum is made 9 times and mass of the bob is made 4 times then the value of time period becomes

168) A simple pendulum is taken from the equator to the pole. Its period

169) There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is T. If the resultant acceleration becomes g/4, then the new time period of the pendulum is

170) The period of a simple pendulum measured inside a stationary lift is found to be T. If the lift starts accelerating upwards with acceleration of g/3, then the time period of the pendulum is

171) Time period of a simple pendulum will be double, if we

172) The velocity of simple pendulum is maximum at

173) A simple pendulum is vibrating in an evacuated chamber, it will oscillate with

174) If a body is released into a tunnel dug across the diameter of earth, it executes simple harmonic motion with time period

175) What effect occurs on the frequency of a pendulum if it is taken from the earth surface to deep into a mine

176) A spring has a certain mass suspended from it and its period for vertical oscillation is T. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is now

177) A spring having a spring constant 'K' is loaded with a mass 'm'. The spring is cut into two equal parts and one of these is loaded again with the same mass. The new spring constant is

178) A particle of mass 200 gm executes S.H.M. The restoring force is provided by a spring of force constant 80 N / m. The time period of oscillations is

179) The length of a spring is l and its force constant is k. When a weight W is suspended from it, its length increases by x. If the spring is cut into two equal parts and put in parallel and the same weight W is suspended from them, then the extension will be

180) A uniform spring of force constant k is cut into two pieces, the lengths of which are in the ratio 1 : 2. The ratio of the force constants of the shorter and the longer pieces is

181) A mass m =100 gms is attached at the end of a light spring which oscillates on a friction-less horizontal table with an amplitude equal to 0.16 metre and time period equal to 2 sec. Initially the mass is released from rest at t = 0 and displacement x = - 0.16 metre. The expression for the displacement of the mass at any time t is

182) A mass m is vertically suspended from a spring of negligible mass; the system oscillates with a frequency n. What will be the frequency of the system if a mass 4 m is suspended from the same spring

183) If the period of oscillation of mass m suspended from a spring is 2 sec, then the period of mass 4m will be

184) A mass m attached to a spring oscillates every 2 sec. If the mass is increased by 2 kg, then time-period increases by 1 sec. The initial mass is

185) If a spring has time period T, and is cut into n equal parts, then the time period of each part will be

186) An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is 15 cm/sec and the period is 628 milli-seconds. The amplitude of the motion in centimeters is

187) When a mass m is attached to a spring, it normally extends by 0.2 m. The mass m is given a slight addition extension and released, then its time period will be

188) A spring executes SHM with mass of 10kg attached to it. The force constant of spring is 10N/m.If at any instant its velocity is 40cm/sec, the displacement will be (where amplitude is 0.5m)

189) Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose, the resultant form of vibration will be

190) Resonance is an example of

191) A simple pendulum is set into vibrations. The bob of the pendulum comes to rest after some time due to

192) A simple pendulum oscillates in air with time period T and amplitude A. As the time passes

193) Two particles executes S.H.M. of same amplitude and frequency along the same straight line. They pass one another when going in opposite directions, and each time their displacement is half of their amplitude. The phase difference between them is

194) A sphere of radius r is kept on a concave mirror of radius of curvature R. The arrangement is kept on a horizontal table (the surface of concave mirror is friction-less and sliding not rolling). If the sphere is displaced from its equilibrium position and left, then it executes S.H.M. The period of oscillation will be

195) A U tube of uniform bore of cross-sectional area A has been set up vertically with open ends facing up. Now m gm of a liquid of density d is poured into it. The column of liquid in this tube will oscillate with a period T such that

196) Two simple pendulums of length 5 m and 20 m respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed oscillations.

197) An ideal spring with spring-constant K is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

198) A disc of radius R and mass M is pivoted at the rim and is set for small oscillations. If simple pendulum has to have the same period as that of the disc, the length of the simple pendulum should be

199) A hollow sphere is filled with water through a small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom, the period of oscillation will

200) Two simple pendulums whose lengths are 100 cm and 121 cm are suspended side by side. Their bobs are pulled together and then released. After how many minimum oscillations of the longer pendulum, will the two be in phase again

201) Which of the following function represents a simple harmonic oscillation

202) A uniform rod of length 2.0 m is suspended through an end and is set into oscillation with small amplitude under gravity. The time period of oscillation is approximately

203) In case of a simple pendulum, time period versus length is depicted by

204) The variation of the acceleration a of the particle executing S.H.M. with displacement y is as shown in the figure

205) A body performs S.H.M. Its kinetic energy K varies with time t as indicated by graph

206) Assertion : All oscillatory motions are necessarily periodic motion but all periodic motion are not oscillatory.
Reason : Simple pendulum is an example of oscillatory motion.

207) Assertion : Simple harmonic motion is a uniform motion.
Reason : Simple harmonic motion is the projection of uniform circular motion.

208) Assertion : Acceleration is proportional to the displacement. This condition is not sufficient for motion in simple harmonic.
Reason : In simple harmonic motion direction of displacement is also considered.

209) Assertion : Sine and cosine functions are periodic functions.
Reason : Sinusoidal functions repeats it values after a definite interval of time.

210) Assertion : The graph between velocity and displacement for a harmonic oscillator is a parabola.
Reason : Velocity does not change uniformly with displacement in harmonic motion.

211) Assertion : When a simple pendulum is made to oscillate on the surface of moon, its time period increases.
Reason : Moon is much smaller as compared to earth.

212) Assertion : Resonance is special case of forced vibration in which the natural frequency of vibration of the body is the same as the impressed frequency of external periodic force and the amplitude of forced vibration is maximum.
Reason : The amplitude of forced vibrations of a body increases with an increase in the frequency of the externally impressed periodic force.

213) Assertion : The graph of total energy of a particle in SHM w.r.t., position is a straight line with zero slope.
Reason : Total energy of particle in SHM remains constant throughout its motion.

214) Assertion : The percentage change in time period is 1.5%, if the length of simple pendulum increases by 3%.
Reason : Time period is directly proportional to length of pendulum.

215) Assertion : Damped oscillation indicates loss of energy.
Reason : The energy loss in damped oscillation may be due to friction, air resistance etc.

216) Assertion : If the amplitude of a simple harmonic oscillator is doubled, its total energy becomes four times.
Reason : The total energy is directly proportional to the square of amplitude of vibration of the harmonic oscillator.

217) Assertion : For an oscillating simple pendulum, the tension in the string is maximum at the mean position and minimum at the extreme position.
Reason : The velocity of oscillating bob in simple harmonic motion is maximum at the mean position.

218) Assertion : The spring constant of a spring is k. When it is divided into n equal parts, then spring constant of one piece is k/n.
Reason : The spring constant is independent of material used for the spring.

219) Assertion : The periodic time of a hard spring is less as compared to that of a soft spring.
Reason : The periodic time depends upon the spring constant, and spring constant is large for hard spring.

220) Assertion : In extreme position of a particle executing S.H.M., both velocity and acceleration are zero.
Reason : In S.H.M., acceleration always acts towards mean position.

221) Assertion : Soldiers are asked to break steps while crossing the bridge.
Reason : The frequency of marching may be equal to the natural frequency of bridge and may lead to resonance which can break the bridge.

222) Assertion : The amplitude of oscillation can never be infinite.
Reason : The energy of oscillator is continuously dissipated.

223) Assertion :The amplitude of an oscillating pendulum decreases gradually with time.
Reason : The frequency of the pendulum decreases with time.

224) Assertion : Consider motion for a mass spring system under gravity, motion of M is not a simple harmonic motion unless Mg is negligibly small.
Reason : For simple harmonic motion acceleration must be proportional to displacement and is directed towards the mean position.

225) A spring with 10 coils has spring constant k. It is exactly cut into two halves, then each of these new springs will have a spring constant

226) The periodic time of a particle doing simple harmonic motion is 4 second. The time taken by it to go from its mean position to half the maximum displacement (amplitude) is

227) The kinetic energy and the potential energy of a particle executing S.H.M. are equal. The ratio of its displacement and amplitude will be

228) Two simple pendulums of lengths 1.44 m and 1 m start swinging together. After how many vibrations will they again start swinging together

229) A particle doing simple harmonic motion, amplitude = 4 cm, time period = 12 sec. The ratio between time taken by it in going from its mean position to 2 cm and from 2 cm to extreme position is

230) On a planet a freely falling body takes 2 sec when it is dropped from a height of 8 m, the time period of simple pendulum of length 1 m on that planet is

231) If a simple pendulum is taken to place where g decreases by 2%, then the time period

232) If a body is executing simple harmonic motion then

233) A particle of mass 200 g executes SHM. The restoring force is provided by a spring of force constant 80 N/m. The time period of oscillation is

234) Displacement between maximum potential energy position and maximum kinetic energy position for a particle executing S.H.M. is

235) The graph between the time period and the length of a simple pendulum is

236) How does time period of a pendulum very with length?

237) To make the frequency double of a spring oscillator, we have to

238) The total energy of a simple harmonic oscillator is proportional to

239) A block is resting on a piston which is moving vertically with SHM of period 1.0 s. At what amplitude of
motion will the block and piston separate?

240) A hollow sphere is filled with water through the small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flow out of the hole at the bottom, the period of oscillation will

241) Two simple pendulum of length 0.5 m and 20 m respectively are given small linear displacement in one
direction at the same time. They will again be in the phase when the pendulum of shorter length has completed… oscillations.

242) The total energy of a particle executing SHM is 80 J. What is the potential energy when the particle is at a
distance of 3/4 of amplitude from the mean position?

243) Consider the following statements :
The total energy of a particle executing simple harmonic motion depends on its
I. Amplitude
II. Period
III. Displacement Of these statements

244) If a watch with a wound spring is taken on to the moon, it

245) What is the effect on the time period of a simple pendulum if the mass of the bob is doubled

246) A body of mass 4 kg hangs from a spring and oscillates with a period 0.5 s on the removel of the body, the spring is shortented by

247) The periodic time of a particle doing simple harmonic motion is 4 s. The taken by it to go from its mean position to half the maximum displacement (amplitude)

248) The ratio of frequencies of two pendulum are 2:3, then their lengths are in ratio

249) A particle is executing S.H.M. Then the graph of acceleration as a function of displacement is

250) Two pendulums of lengths 1m and 1.21m respectively start swinging together with same amplitude. The
number of vibrations that will be executed by the longer pendulum before the two will swing together again are

251) The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming
out, the time period of oscillation would

252) A pendulum clock is placed on the moon, where object weighs only one-sixth as much as on earth, how
many seconds the clock tick out in an actual time of 1 minute the clock keeps good time on earth?

253) Which one of the following is a simple harmonic motion

254) The bob of a simple pendulum of length L is released at time t = 0 from a position of small angular displacement. Its linear displacement at time t is given by

255) Two particles execute SHM of the same amplitude and frequency along the same straight line. If they pass one another when going in opposite directions, each time their displacement is half their amplitude, the phase difference between them is

256) Two particles executes S.H.M. of same amplitude and frequency along the same straight line. They pass one another when going in opposite directions, and each time their displacement is half of their amplitude. The phase difference between them is

257) A particle executing a simple harmonic motion has a period of 6 s. The time taken by the particle to move from the mean position to half the amplitude, starting from the mean position is

258) The circular motion of a particle with constant speed is

259) The average acceleration of a particle performing SHM over one complete oscillation is

260) A tunnel is made across the earth of radius R, passing through its centre. A ball is dropped from a height h in the tunnel. The motion will be periodic with time period.

261) A particle of mass 1 kg is moving in SHM with an amplitude 0.02 m and a frequency of 60 Hz. The maximum force in newton acting on the particle is

262) The restoring force of SHM is maximum when particle

263) A particle is executing simple harmonic motion with an amplitude A and time period T. The displacement of the particle after 2T period from its initial position is

264) A particle is executing SHM with amplitude a. when the PE of a particle is one-fourth of its maximum value
during the oscillation, its displacement from the equilibrium position will be

265) The potential energy of a simple harmonic oscillator when the particle is half way to its end point is
(where E is the total energy)

266) If the displacement equation of a particle be represented by y = A sin PT + B cos PT, the particle executes

267) A uniform spring of force constant k is cut into two pieces whose lengths are in the ratio of 1:2.
What is the force constant of second piece in terms of k?

268) A particle is subjected simultaneously to two SHM’s one along the x-axis and the other along the
y-axis. The two vibrations are in phase and have unequal amplitudes. The particle will execute

269) A mass of 10 kg is suspended from a spring balance. It is pulled aside by a horizontal string so that it
makes angle of 60° with the vertical. The new reading of the balance is

270) Two identical pendulum are oscillating with amplitudes 4 cm and 8 cm. the ratio of their energies of oscillation will be

271) U is the PE of an oscillating particle and F is the force acting on it at a given instant. Which of the following is true?

272) A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The frequency of its oscillation is

273) A particle executes S.H.M. with a period of 6 second and amplitude of 3 cm. Its maximum speed in cm/s is

274) A large horizontal surface moves up and down in SHM with an amplitude of 1 cm. if a mass of 10 kg (which is placed on the surface) id to remain continuously is in contact with it. The maximum frequency of SHM will be

275) A mass M, attached to a spring, Oscillates with a period of 2 s. If the mass is increased by 4 kg, the time period increases by 1 s. Assuming that Hooke’s law is obeyed, the initial mass M was

276) A body having natural frequency v′ is executing forced oscillations under a driving force of frequency. The system will vibrate

277) A particle of mass m is located in a one dimensional potential field where potential energy is given by (x)=A(1−cospx) , where A and p are constants. The period of small oscillations of the particle is

278) The displacement of a particle executing SHM is given by y=0.25 sin 200t cm. the maximum speed of the particle is

279) A particle of mass 10 g is describing S.H.M. along a straight line with period of 2 s and amplitude of 10 cm. Its kinetic energy when it is at 5 cm from its equilibrium position is

280) In case of a forced vibration, the resonance wave becomes very sharp when the

281) If a spring extends by x on loading then the energy stored in the spring is (if T is the tension and k is the force constant of the of the spring).

282) A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilibrium to the end is

283) The period of oscillation of a mass m suspended from a spring is 2 s. If along with it another mass 2 kg is also suspended, the period of oscillation increases by 1 s. the mass m will be

284) The motion which is not simple harmonic is

285) A man measures the period of a simple pendulum inside a stationary lift ad finds it to be T second. If the lift accelerates upwards with an acceleration g/4, then the period of pendulum will be

286) A uniform cylinder of length L and mass M having cross sectional area A is suspended with its vertical length, from a fixed point by a massless spring, such that it is half submerged in a liquid of density d at equilibrium position. When released, it starts oscillating vertically with a small amplitude. If the force constant of the spring is k, the frequency of oscillation of the cylinder is

287) A S.H.M. has amplitude ′a′ and time period T. The maximum velocity will be

288) Which of the following combination of Lissajous’ figure will be like eight (8)?

289) A girl swings on cradle in a sitting position. If she stands what happens to the time period of girl and cradle?

290) The displacement of a particle of mass 3 g executing simple harmonic motion is given by Y=3 sin (0.2t) in SI units. The KE of the particle at a point which is at a distance equal to 1/3 of its amplitude from its mean position is

291) When the amplitude of a body executing SHM become twice what happens?

292) The length of simple pendulum is increased by 1%. Its time period will

293) A particle starts SHM form the mean position. Its amplitude is a and total energy E. At one instant its kinetic energy is 3 E/4 its displacement at this instant is

294) In SHM restoring force is F=−k x, where k is force constant, x is displacement and A is amplitude of motion, then total energy depends upon

295) When the kinetic energy of a body executing S.H.M. is 1/3 of the potential energy. The displacement of the body is x percent of the amplitude, where x is

296) A particle moving along the x-axis executes simple harmonic motion, then the force acting on it is given by

297) A particle is executing SHM with amplitude a. When the PE of a particle is one-fourth of its maximum value during the oscillation, its displacement from the equilibrium position will be

298) A second’s pendulum is placed in a space laboratory orbiting around the earth at a height 3R, where R is the radius of the earth. The time period of the pendulum is

299) A particle of amplitude A is executing simple harmonic motion. When the potential energy of particle is half of its maximum potential energy, then displacement from its equilibrium position is

300) A body executes simple harmonic motion. The potential energy (PE), the kinetic energy (KE) and total energy (TE) are measured as function of displacement x. Which of the following statement is true?

301) The height of a swing changes during its motion from 0.1 m to 2.5 m. The minimum velocity of a boy who swings in this swing is

302) The time period of a simple pendulum, when it is made to oscillate on the surface of moon

303) Two points are located at a distance of 10 m and 15 m from the source of oscillation. The period of oscillation is 0.05 sec and the velocity of the wave is 300 m/sec. What is the phase difference between the oscillations of two points

304) Infinite springs with force constants k,2k,4k and 8k….. respectively are connected in series. The effective force constant of the spring will be

305) For a simple pendulum the graph between L and T will be

306) In simple harmonic motion, the ratio of acceleration of the particle to its displacement at any time is a measure of

307) A particle executes SHM of amplitude 25 cm and time period 3 s. What is the minimum time required for the particle to move between two points 12.5 cm on either side of the mean position?

308) Two identical blocks A and B, each of mass m resting on smooth floor, are connected by a light spring of natural length L and the spring constant k, with the spring at its natural length. A third identical block at C (mass m) moving with a speed (v) along the line joining A and B collides with A. The maximum compression in the spring is proportional to

309) The KE and PE of a particle executing SHM of amplitude a will be equal when displacement is

310) A particle is vibrating in a simple harmonic motion with an amplitude of 4 cm. At what displacement from the equilibrium position, is its energy half potential and half kinetic

311) Graph between velocity and displacement of a particle, executing S.H.M. is

312) Ratio of kinetic energy at mean position to potential energy at A/2 of a particle performing SHM

313) The acceleration of a particle in S.H.M. is

314) Two pendulums of length 212 cm and 100 cm start vibrating. At same instant the two are in the mean position in the same phase. After how many vibrations of the shorter pendulum, the two will be in phase in the mean position?

315) A particle executes linear simple harmonic motion with an amplitude of 2 cm. When the particle is at 1 cm from the mean position the magnitude of its velocity is equal to that of its acceleration. Then its time period in second is

316) The period of a simple pendulum inside a stationary lift is T. The lift accelerates upwards with an acceleration of g/s. The time period of pendulum will be

317) The total energy of a particle executing S.H.M. is proportional to

318) The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal, when displacement

319) A simple pendulum, suspended from the ceiling of a stationary van, has time period T. If the van starts moving with a uniform velocity the period of the pendulum will be

320) How does the time period of pendulum vary with length

321) A plate oscillates with time period ′T′. Suddenly, another plate put on the first time, then time period

322) The maximum velocity of a particle executing SHM is V. If the amplitude is doubled and the time period of oscillation decreased to 1/3 of its original value, the maximum velocity becomes

323) If the length of second’s pendulum is increased by 2% How many seconds it will lose per day?

324) A simple harmonic oscillator has an amplitude a and time period T. The time required by it to travel from x=a to x=a/2 is

325) When the displacement is half the amplitude, the ratio of potential energy to the total energy is

326) A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of

327) Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose, the resultant from of vibration will be

328) For Simple Harmonic Oscillator, the potential energy is equal to kinetic energy

329) A light spiral spring supports a 200 g weight at its lower end. It oscillates up and down with a period of 1 s. How much weight (in gram) must be removed from the lower end to reduce the period to 0.5 s?

330) An elastic string has a length l when tension in it is 5 N. Its length is h when tension is of 4 N. on subjecting the string to a tension of 9 N, its length will be

331) If a simple pendulum oscillates with an amplitude of 50 mm and time period of 2 s, then its maximum velocity is

332) When the displacement is half of the amplitude, then what fraction of the total energy of a simple harmonic oscillator is kinetic?

333) The time period of a mass suspended from a spring is 5 s. The spring is cut into four equal parts and the same mass is now suspended from one of its parts. The period is now

334) Which of the following equations does not represent a simple harmonic motion

335) Two simple harmonic motions of angular frequency 100 and 1000 rad/s have the same displacement amplitude. The ratio of their maximum acceleration is

336) An ideal spring with spring constant K=200 N/m is fixed on one end on a wall. If the spring is pulled with a force 10 N at the other end along its length, how much it will extended?

337) Masses m and 3 m are attached to the two ends of a spring of constant k. If the system vibrates freely. The period of oscillation will be

338) In a simple harmonic motion maximum velocity is at

339) In a simple harmonic oscillator, at the mean position

340) What is time period of pendulum hanged in satellite?
(T is time period on earth)

341) In a simple pendulum, the period of oscillation T is related to length of the pendulum l as

342) The time period of a simple pendulum is 2 s. If its length is increased 4 times, then its period becomes

343) Acceleration of a particle, executing SHM, at it’s mean position is

344) Which one of the following equations does not represent SHM, x = displacement and t = time. Parameters a, b and c are the constants of motion?

345) A weightless spring which has a force constant k oscillates with frequency n when a mass m is suspended from it. The spring is cut into two equal halves and a mass 2 m is suspended from one part of spring. The frequency of oscillation will now become

346) Average value of KE and PE over entire time period is

347) A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The
minimum time taken by the particle to travel half of the amplitude from the equilibrium is

348) Two equal negative charge –q are fixed points (0, a) and (0,-0) on the Y-axis. A positive charge Q is
released from rest at point (2a, 0) on the X-axis. The charge Q will

349) A point mass m is suspended at the end of a massless wire of length L and cross-section area A. If
Y is the Young’s modulus for the wire, then the frequency of oscillations for the SHM along the
vertical line is

350) When a mass M is attached to the spring of force constant k, then the spring stretches by l. If the mass oscillates with amplitude l, what will be maximum potential energy stored in the spring

351) A simple pendulum is attached to the roof of a lift. If time period of oscillation, when the lift is stationary is T. Then frequency of oscillation, when the lift falls freely, will be

352) The period of oscillation of a simple pendulum of constant length at earth surface is T. Its period inside a mine is

353) In a seconds pendulum, mass of the bob is 30 g. If it is replaced by 90 g mass, then its time period
will be

354) A heavy brass sphere is hung from a weightless inelastic spring and as a simple pendulum its timeperiod of oscillation is T. When the sphere is immersed in a non-viscous liquid of density 1/10 that of brass, it will act as a simple pendulum of period

355) A system exhibiting S.H.M. must possess

356) The time period of the variation of potential energy of a particle executing SHM with period T is

357) The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is

358) The potential energy of a particle executing S.H.M. is 2.5 J, when its displacement is half of amplitude. The total energy of the particle be

359) The amplitude of a particle executing SHM is made three-fourth keeping its time period constant. Its total energy will be

360) A simple harmonic oscillator has a period T and energy E. the amplitude of the oscillator is doubled. Choose the correct answer.

361) In S.H.M. maximum acceleration is at

362) If two springs A and B with spring constants 2 k and k, are stretched separately by same suspended weight, then the ratio between the work done in stretched A and B is

363) The differential equation of a particle executing SHM along y-axis is

364) The velocity of a particle performing simple harmonic motion, when it passes through its mean position is

365) A body is executing S.H.M. When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocity of the body is 10 cm/s and 8 cm/s. Then the time period of the body is

366) A particle doing simple harmonic motion, amplitude =4 cm, time period =12 s. The ratio between time taken by it in going from its mean position to 2 cm and from 2 cm to extreme position is

367) The velocity of particle in simple harmonic motion at displacement y from mean position is

368) Two particles A and B execute simple harmonic motion of period T and 5T/4 They start from mean position. The phase difference between them when the particle A complete an oscillation will be

369) A lift is ascending with an acceleration equal to g/3. Its time period of oscillation isT. What will be the time period of a simple pendulum suspended from its ceiling in stationary lift?

370) The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage increase in the time period of the pendulum of increased length is

371) The time period of a particle in simple harmonic motion is 8 seconds. At t=0, it is at the mean position. The ratio of the distances travelled by it in the first and second seconds is

372) Choose the correct statement :

373) The period of particle in linear SHM is 8 s. At t=0, it is at the mean position. The ratio of the distances
travelled by it in Its second and 2nd second is

374) A particle is having kinetic energy 1/3 of the maximum value at a distance of 4 cm from the mean position,
Find the amplitude of motion.

375) The displacement y in cm is given in terms of time t sec by the equation
y = 3 sin 314t + 4 cos314t
The amplitude of SHM is

376) The magnitude of maximum acceleration is π times that of maximum velocity of a simple harmonic oscillator. The time period of the oscillator in second is

377) Starting from the origin a body oscillates simple harmonically with a period of 2 s. After what
time will its kinetic energy be 75% of the total energy?

378) Which of the following function represents a simple harmonic oscillation

379) If the period of oscillation of mass m suspended from a spring is 2 s, then the period of mass 4m will be

380) A horizontal plank has a rectangular block placed on it. The plank stars oscillating vertically and simple harmonically with an amplitude of 40 cm. the block just loses contact with the plank when the later is momentary at rest. Then

381) If a simple pendulum is taken to a place where g decreases by 2% then the time period

382) The total energy of the body executing S.H.M. is E. Then the kinetic energy when the displacement is half of the amplitude, is

383) A spring (spring constant =k) is cut into 4 equal parts and two parts are connected in parallel. What is the effective spring constant?