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Simple harmonic Motion, , Section 1, , x(t)  Asin, , t, 90, , . The ratio of kinetic to potential, , energy of the particle at t = 210 s will be, , 1, 9, , (a) 1/ 2, , (b), , (c) 1/3, , (d) 1, , 4. A particle executes simple harmonic motion with an, amplitude of 5 cm. When the particle is at 4 cm from, the mean position, the magnitude of its velocity in SI, units is equal to that of its acceleration., Then, its periodic time in seconds is., (a), , 7, , 3, , (b), , 3, , 8, , (c), , 4, 3, , (d), , 8, 3, , Level0, 1. When the potential energy of a particle executing, simple harmonic motion is one-fourth of its, maximum value during the oscillation, the, displacement of the particle from the equilibrium, position in terms of its amplitude a is:, (a) a/4, (b) a/3, (c) a/2, (d) 2a/3, 2. The amplitude of a particle executing SHM is 4 cm., At the mean position, the speed of the particle is 16, cm/s. The distance of the particle from the mean, position at which the speed of the particle becomes, , 5. A particle is executing simple harmonic motion, (SHM) of amplitude A, along the x-axis, about x = 0., When its potential Energy (PE) equals kinetic energy, (K.E.) the position of the particle will be:, (a), , A, 2, (c), , 3 cm, , (a) 1 cm, , (b), , (c) 2 cm, , (d) 2 3 cm, , 3. A particle is undergoing simple hormonic motion has, time dependent displacement given by, , A, 2, , A, 2 2, , (d) A, , 6. Average velocity of a particle executing SHM in one, complete vibration is: ], , A, 2, A 2, (c), 2, (a), , 8 3 cm/s is:, , (b), , (b) A, (d) Zero, , 7. The distance covered by a particle undergoing SHM, in one time period is (amplitude = A), (a) zero, (b) A, (c) 2A, (d) 4A

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8. A simple pendulum performs simple harmonic motion, about X = 0 with an amplitude A and time period T., , particle at t = 4 / 3 s is, , The speed of the pendulum at X =, (a), , (b), , (c), , (a), , (d), , 9. A particle is moving with constant angular velocity, along the circumference of a circle. Which of the, following statements is true, (a) The particle so moving executes S.H.M., (b) The projection of the particle on any one of the, diameters executes S.H.M, (c) The projection of the particle on any of the, diameters executes S.H.M., 10. The maximum velocity of a simple harmonic motion, represented by y = 2 sin, (a) 200, , is given by, , (b), , (c) 100, , (c), , 3 2,  cm / s 2, 32, , 2, 32, , (b), ,  2, cm / s 2, 32, , (d) , , cm / s 2, , 3 2,  cm / s 2, 32, , 18. A body is executing simple Harmonic Motion. At a, displacement x its potential energy is E1 and at a, displacement y its potential energy is E2. The potential, energy E at displacement (x + y) is, (a), (b), (c) E = E1 + E2, (d) E= E1 + E 2, 19. The function x= sin2 (ωt) represents, (a) a periodic, but not simple harmonic motion, , (d), , with a period π/ω, 11. A particle starts S.H.M. from the mean position. Its, amplitude is A and time period is T. At the time when, its speed is half of the maximum speed, its, displacement y is, (a), , (b), , (c), , (d), , 12. The maximum velocity and the maximum, acceleration of a body moving in a simple harmonic, oscillator are 2m/s and 4m/s2. Then angular frequency, will be, (a)3rad/sec (b) 0.5rad/sec (c) 1rad/sec (d) 2rad/sec, 13. Particle of mass 10 grams is executing simple, harmonic motion with an amplitude of 0.5 m and, periodic time of (π/5) seconds. The maximum value of, the force acting on the particle is, (a) 25 N, (b) 5 N, (c) 2.5 N, (d) 0.5 N, , b) a periodic, but not simple harmonic motion, with a period 2 π/ω, (c) a simple harmonic motion with a period π/ω, (d) a simple harmonic motion with a period 2π/ω, 20.A particle starts oscillating simple harmonically from, its equilibrium position. Then the ratio of kinetic and, T, potential energy of the particle at time, is, 12, (T = time period), (a)2:1, , (b) 3:1, , (c) 4:1, , (d) 1:4, , 21. The radius of circle the period of revolution initial, position and sense of revolution are indicated in the, fig., , 14.The displacement of a particle in simple harmonic, motion in one time period is, (a) A, (b) 2A, (c) 4A, (d) zero, 15. The total energy of particle, executing simple, harmonic motion is, (a) independent of x, , (b)  x2 (c)  x, , (d)  x1/2, , 16. A particle starts simple harmonic motion from the, mean position. Its amplitude is α and total energy E., At one instant its kinetic energy is 3E/4. Its, displacement at that instant is, (a) α/, (b) α/2, (c), (d) α/ 3, 17. The x-t graph of a particle undergoing simple, harmonic motion is, x, shown below. The, 1, acceleration of the, x(cm), , 4, -1, , 8, , 12 t Sec, , y-projection of the radius vector of rotating, particle P is:, (a) y(t)  3cos 2 t, where y in m, ,  t ,  , where y in m,  2,  3 t , (c) y (t)  3cos ,  , where y in m,  2 ,  t , (d) y (t)  3cos   , where y in m,  2, (b) y (t)  4sin 

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22. Maximum speed of a particle in simple harmonic, motion is vmax. Then average speed of a particle in, SHM is equal to, v, v, 2v, v, (a) max, (b) max (c) max (d) max, 2, , , 2, Section 2 Source of SHM (Pendulum Spring etc.), , 26. What is the effect on the time period of a simple, pendulum if the mass of the bob is doubled:, (a) Halved, (b) Doubled, (c) Becomes eight times (d) No effect, 27. 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:, (a) Increase, (b) Decreases, (c) Remain unaffected (d) Becomes infinite, 28. A simple pendulum is suspended from the roof of a, trolley which moves in a horizontal direction with an, acceleration a, then the time period is given by, , 1, , where g’ is equal to:, g', , T  2, , 23. A simple pendulum has a legth l. The mass of the, bob is m. The bob is given a charge +q. The, pendulum is suspended between the plates of a, charged parallel plate capacitor which are placed, vertically. If E is the electric field intensity between, the plates, then the time period of oscillation will be:, (a) 2, (c) 2, , l, g, l, g  qE / m, , (b) 2, (d) 2, , l, g  qE / m, I, 2, [g  (qE/ m)2 ]1/2, , 24. A body of mass 0.01 kg executes simple harmonic, motion (S.H.M) about x = 0 under the influence of a, force shown below. The period of the S.H.M is:, , (a) g, , (b) g – a, , (c) g + a, , (d), , 29. If the length of second’s pendulum is increased by, 2% how many seconds it will lose per day:, (a) 3927 s, (b) 3727 s, (c) 3427 s, (d) 864 s, , 30. If the length of the simple pendulum is increased by, 44% then what is the change is time period of, pendulum., (a) 22% (b) 20% (c) 33% (d) 44%, 31. A simple pendulum consisting of a ball off mass m, tied to a thread of length l is made to swing on a, circular arc of angle  in a vertical plane. At the end, of this arc, another ball of mass m is placed at rest., The momentum transferred to this ball at rest by the, swinging ball is:, , (c), , (b) 0.52 s, (d) 0.30 s, , 25. If a hole is bored along the diameter of the earth and, a stone is dropped into hole:, (a) The stone reaches the centre of the earth and, stops there, (b) The stone reaches the other side of the earth, of stops, (c) The stone executes simple harmonic motion, about the centre of the earth, (d) The stone reaches the other side of the earth, and escapes into space., , m, l, , g, l, , (b) m, , (a) Zero, , (a) 1.05 s, (c) 0.25 s, , g 2  a2, , l, g, , (d), , m, l, 2, l, g, , 32. The periodic time of a simple pendulum of length 1, m and amplitude 2 cm is 5 seconds. If the amplitude, is made 4 cm, its periodic time in seconds will be:, (a) 2.5, (b) 5, (c) 10, (d) 5 2, 33. The time periodic of a simple pendulum of length L, as measured in an elevator descending with, acceleration, (a) 2, , g, is:, 3, 3L, g, ,  3L , ,  g , , (b)  

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 3L , (c) 2  , ,  2g , , 2L, (d) 2, 3g, , 34. What effect occurs on the frequency of a pendulum, if it is taken from the earth surface to deep into a, mine:, (a) Increases, (b) Decreases, (c) First increases then decreases, (d) None of these, 35. A simple pendulum has a time period T in vacuum., Its time period when it is completely immersed in a, liquid of density one – eight of the density of, material of the bob is, , 7, T (b), 8, , (a), , 5, T (c), 8, , 3, T, 8, , (d), , 8, T, 7, , 36. The frequency of oscillation of a simple pendulum of, length L, mounted in a cabin that is failing freely, under gravity is, (a) infinity, (b) zero, (c), , g, 2L, , (d), , g, L, , 37. The minimum time taken by a particle executing, SHM of period T to move from the equilibrium, position to half the amplitude is:, (a) T/4, (b) T/2, (c) T/8, (d) T/12, 38. A simple harmonic oscillator consist of a particle of, mass m and ideal spring with spring constant k. The, particle oscillates with a time period T. The spring is, cut into two equal parts. If one part oscillates with, the same particle, the time period will be:, (a) T/2, (b) T / 2, (c), , 2T, , (d) 2T, , 39. A simple pendulum of length L and mass m is, vibrating with an amplitude a. Then the maximum, tension in the string is:, ,   a 2 , (b) mg 1    ,   L  , , (a) mg, , a , , (c) mg 1 ,  2 L , , 2, , a, , (d) mg 1  ,  L1 , , 2, , 40. A person measures the time period of a simple, pendulum inside a stationary lift finds it to be T. If, the lift starts accelerating upwards with an, acceleration g/3, the period of the pendulum will be:, (a), , 3T, , (c), , 3, T, 2, , 41. The mass and the diameter of a planet are three times, the respective values for the Earth. The period of, oscillation of a simple pendulum on the Earth is 2s., The period of oscillation of the same pendulum on, the planet would be:(a), , 2, s, 3, , (b) 2 3s, , (c), , 3, s, 2, , (d), , 3, s, 2, , 42. A mass falls from a height ‘h’ and its time of fall ‘t’, is recorded in terms of time period T of a simple, pendulum On the surface of earth it is found that t –, 2T. The entire set up is taken on the surface of, another planet whose mass is half of that of earth and, radius the same. Same experiment is repeated and, corresponding times noted as t’ and T’., (a) t '  2 T ', (c) t '  2T ', , (b) t '  2T ', (d) t '  2T ', , 44. If a hole is bored along the diameter of the earth and, a stone is dropped into the hole, (a) The stone reaches the centre of the earth and stops, there, (b) The stone reaches the other side of the earth and, stops there, (c) The stone executes simple harmonic motion about, the centre of earth, (d) The stone reaches the other side of the earth and, escapes into space, 45., A pendulum clock that keeps correct time on the, earth is taken to the moon. It will run, (a) at correct rate, (b) 6 times faster, (c) 6 times faster, (d) 6 times slower, 46. A wall clock uses a vertical springmass system to, measure the time. Each time the mass reaches an, extreme position, the clock advances by a second. The, clock gives correct time at the equator. If the clock is, taken to the poles it will, (a) run slow, (b) run fast, (c) stop working, (d) given correct time, 47., Acceleration-displacement graph of a particle, executing SHM is as, a(m/s², shown in the figure., The time period of its, oscillation is (in sec), ), (a) /2, (b) 2, 45o, (c) , (d) /4, x(m), , (b) T / 3, (d) T/3, , 48. 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

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(a) K/2, 49., , (b) K, , (c) 2K, , (d) K2, , Angular SHM, , A child swinging on a swing in sitting position,, stands up, then the time period of the swing will, (a) increase (b) decrease, (c) remains same, (d) increase of the child is along and decreases if, the child is short, , Level1, 50., , A mass M is suspended from a spring of, negligible mass. The spring is pulled a little and, then released so that the mass executes SHM of, time period T. If the mass is increased by m, the, time period becomes 5T/3. then the ratio of m/M is, (a) 3/5, (b) 25/9, (c) 16/9, (d) 5/3, , 51.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, (a) 11%, (b) 21%, (c) 42%, (d) 10%, 52.A particle at the end of a spring executes simple, harmonic motion with a period t1, while the, corresponding period for another spring is t2. If the, period of oscillation with the two springs in series is t,, then, (a) T 1  t11  t 21, (b) T2  t12  t 22, (c) T = t1 + t2, (d) T 2  t12  t 22, 53. Two springs, of force constants k1 and k2 are, connected to a mass, m as shown. The, frequency of, oscillation of the, mass is f. If both k1 and k2 are, made four times their original values, the frequency, of oscillation becomes, (a) 2 f, (b) f / 2, (c) f / 4, (c) 4 f, O, 54. A pendulum has time period T, for small oscillations. An, obstacle P is situated below the, l, point of suspension O at a, 3l, distance, . The pendulum is, 4, P, released from rest. Throughout, the motion the moving string makes small angle with, vertical. Time after which the pendulum returns back, to its initial position is, 4T, 3T, 5T, (a) T, (b), (c), (d), 4, 4, 3, , 55. A pendulum is fixed on a cart sliding without friction, down an inclined plane of inclination  with, horizontal. The period of oscillation of pendulum is, l, l, l, l, (a) 2, (b) 2, (c) 2, (d) 2, g cos , g, sin , tan , , 56. Two light identical springs of spring constant k are, attached horizontally at the two ends of a uniform, horizontal rod AB of length l and mass m. The rod is, pivoted at its centre ‘O’ and can rotate freely in, horizontal plane. The other ends of the two springs, are fixed to rigid supports as shown in fig. The rod is, gently pushed through a small angle and released., The frequency of resulting oscillation is:, , (a), , 1, 2, , 6k, m, , (b), , 1, 2, , 2k, m, , (c), , 1, 2, , k, m, , (d), , 1, 2, , 3k, m, , ....By Praveen Gupta