Tiêu đề 15. Simple Harmonic Motion Easy.pdf ✅

1. 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) 2 A (b) 2 A (c) 2 A 3 (d) 3 2 A 2. The amplitude and the periodic time of a S.H.M. are 5cm and 6sec respectively. At a distance of 2.5cm away from the mean position, the phase will be (a) 5 / 12 (b)  / 4 (c)  / 3 (d)  / 6 3. Two equations of two S.H.M. are y = a sin( t −) and y = b cos( t −) . The phase difference between the two is (a) 0° (b) ° (c) 90° (d) 180° 4. The amplitude and the time period in a S.H.M. is 0.5 cm and 0.4 sec respectively. If the initial phase is  / 2 radian, then the equation of S.H.M. will be (a) y = 0.5 sin 5t (b) y = 0.5 sin 4t (c) y = 0.5 sin 2.5t (d) y = 0.5 cos 5t 5. The equation of S.H.M. is y = a sin(2nt +) , then its phase at time t is (a) 2nt (b)  (c) 2nt + (d) 2t 6. A particle is oscillating according to the equation X = 7 cos 0.5t , where t is in second. The point moves from the position of equilibrium to maximum displacement in time (a) 4.0 sec (b) 2.0 sec (c) 1.0 sec (d) 0.5 sec 7. 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 (a) T / 6 (b) T / 4 (c) T / 3 (d) T / 2 8. A kg 20 1.00 10 −  particle is vibrating with simple harmonic motion with a period of sec 5 1.00 10 −  and a maximum speed of 1.00 10 m/s 3  . The maximum displacement of the particle is (a) 1.59 mm (b) 1.00 m (c) 10 m (d) None of these 9. The phase (at a time t) of a particle in simple harmonic motion tells (a) Only the position of the particle at time t (b) Only the direction of motion of the particle at time t (c) Both the position and direction of motion of the particle at time t (d) Neither the position of the particle nor its direction of motion at time t 10. 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. (d) None of the above 11. A particle is executing simple harmonic motion with a period of T seconds and amplitude a metre. The shortest time it takes to reach a point m a 2 from its mean position in seconds is (a) T (b) T/4 (c) T/8 (d) T/16 12. A simple harmonic motion is represented by F(t) = 10 sin(20 t + 0.5) . The amplitude of the S.H.M. is (a) a = 30 (b) a = 20 (c) a = 10 (d) a = 5 13. Which of the following equation does not represent a simple harmonic motion (a) y = a sin t (b) y = a cos  t (c) y = asint + b cost (d) y = a tan  t 14. A particle in S.H.M. is described by the displacement function x(t) = a cos(t +) . If the initial (t = 0) position of the particle is 1 cm and its initial velocity is  cm/s . The angular frequency of the particle is  rad / s , then it’s amplitude is (a) 1 cm (b) 2 cm (c) 2 cm (d) 2.5 cm 15. A particle executes a simple harmonic motion of time period T. Find the time taken by the particle to go directly from its mean position to half the amplitude (a) T / 2 (b) T / 4 (c) T / 8 (d) T / 12
16. A particle executing simple harmonic motion along y-axis has its motion described by the equation y = A sin( t)+ B . The amplitude of the simple harmonic motion is (a) A (b) B (c) A + B (d) A + B 17. 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 (a) 1 sec (b) 1/3 sec (c) 2/3 sec (d) 3 / 2 sec 18. Which one of the following is a simple harmonic motion (a) Wave moving through a string fixed at both ends (b) Earth spinning about its own axis (c) Ball bouncing between two rigid vertical walls (d) Particle moving in a circle with uniform speed 19. A particle is moving in a circle with uniform speed. Its motion is (a) Periodic and simple harmonic (b) Periodic but not simple harmonic (c) A periodic (d) None of the above 20. Two simple harmonic motions are represented by the equations       = + 3 1 0.1 sin 100  y  t and 0.1 cos . 2 y =  t The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is (a) 3 − (b) 6  (c) 6 − (d) 3  21. Two particles are executing S.H.M. The equation of their motion are , 4 1 10 sin       = + T y t           = + 4 3 25 sin 2 T y t   . What is the ratio of their amplitude (a) 1 : 1 (b) 2 : 5 (c) 1 : 2 (d) None of these 22. 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 (a) 8 1 sec (b) 6 1 sec (c) 4 1 sec (d) 3 1 sec 23. A system exhibiting S.H.M. must possess (a) Inertia only (b) Elasticity as well as inertia (c) Elasticity, inertia and an external force (d) Elasticity only 24. If       = + 6 sin  x a t and x  = a cost , then what is the phase difference between the two waves (a)  / 3 (b)  / 6 (c)  / 2 (d)  25. A simple pendulum performs simple harmonic motion about X = 0 with an amplitude A and time period T. The speed of the pendulum at 2 A X = will be (a) T A 3 (b) T A (c) T A 2  3 (d) T A 2 3 26. A body is executing simple harmonic motion with an angular frequency 2rad / s . The velocity of the body at 20 mm displacement, when the amplitude of motion is 60 mm, is (a) 40 mm /s (b) 60mm / s (c) 113 mm / s (d) 120 mm / s 27. 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 (a) 5 (b) 5 2 (c) 5 3 (d) 10 2 28. A simple harmonic oscillator has a period of 0.01 sec and an amplitude of 0.2 m. The magnitude of the velocity in 1 sec − m at the centre of oscillation is (a) 20 (b) 100 (c) 40 (d) 100 29. A particle executes S.H.M. with a period of 6 second and amplitude of 3 cm. Its maximum speed in cm/sec is (a)  / 2 (b)  (c) 2 (d) 3 30. 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
(a)  m / s (b) 2 m / s (c) 2 m / s (d) 4 m / s 31. A S.H.M. has amplitude ‘a’ and time period T. The maximum velocity will be (a) T 4a (b) T 2a (c) T a 2 (d) T 2a 32. 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/sec and 8 cm/sec. Then the time period of the body is (a) 2 sec (b)  / 2 sec (c)  sec (d) 3 / 2 sec 33. A particle has simple harmonic motion. The equation of its motion is       = − 6 5 sin 4  x t , where x is its displacement. If the displacement of the particle is 3 units, then it velocity is (a) 3 2 (b) 6 5 (c) 20 (d) 16 34. If a simple pendulum oscillates with an amplitude of 50 mm and time period of 2 sec, then its maximum velocity is (a) 0.10 m / s (b) 0.15 m / s (c) 0.8 m / s (d) 0.26 m / s 35. If the displacement of a particle executing SHM is given by y = 0.30 sin(220 t + 0.64 ) in metre, then the frequency and maximum velocity of the particle is (a) 35 Hz, 66 m / s (b) 45 Hz, 66 m / s (c) 58 Hz, 113 m / s (d) 35 Hz, 132 m / s 36. The maximum velocity and the maximum acceleration of a body moving in a simple harmonic oscillator are 2 m/s and 4 / . 2 m s Then angular velocity will be (a) 3 rad/sec (b) 0.5 rad/sec (c) 1 rad/sec (d) 2 rad/sec 37. If a particle under S.H.M. has time period 0.1 sec and amplitude m 3 2 10 −  . It has maximum velocity (a) m/s 25  (b) m/s 26  (c) m/s 30  (d) None of these 38. A particle executing simple harmonic motion has an amplitude of 6 cm. Its acceleration at a distance of 2 cm from the mean position is 2 8 cm/s . The maximum speed of the particle is (a) 8 cm/s (b) 12 cm/s (c) 16 cm/s (d) 24 cm/s 39. 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 (a) 3 cm (b) 5 cm (c) 2( 3) cm (d) 2( 5 ) cm 40. 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 (a) 1 : 2 (b) 2 : 1 (c) 2 : 3 (d) 3 : 2 41. A particle is performing simple harmonic motion with amplitude A and angular velocity . The ratio of maximum velocity to maximum acceleration is (a)  (b) 1/ (c)  2 (d) A 42. The angular velocities of three bodies in simple harmonic motion are ω1 , ω2 , ω3 with their respective amplitudes as A1 ,A2 ,A3 . If all the three bodies have same mass and velocity, then (a) A1ω1 = A2ω2 = A3ω3 (b) A1ω1 2 = A2ω2 2 = A3ω3 2 (c) A1 2ω1 = A2 2ω2 = A3 2ω3 (d)A1 2ω1 2 = A2 2ω2 2 = A 2 43. The velocity of a particle performing simple harmonic motion, when it passes through its mean position is (a) Infinity (b) Zero (c) Minimum (d) Maximum 44. The velocity of a particle in simple harmonic motion at displacement y from mean position is (a) ω√a 2 + y 2 (b) ω√a 2 − y 2 (c) ωy (d) ω2√a 2 − y 2 45. A particle is executing the motion x = A cos( t −) . The maximum velocity of the particle is (a) A cos (b) A (c) A sin (d) None of these 46. A particle executing simple harmonic motion with amplitude of 0.1 m. At a certain instant when its displacement is 0.02 m, its
acceleration is 0.5 m/s2 . The maximum velocity of the particle is (in m/s) (a) 0.01 (b) 0.05 (c) 0.5 (d) 0.25 47. The amplitude of a particle executing SHM is 4 cm. At the mean position the speed of the particle is 16 cm/sec. The distance of the particle from the mean position at which the speed of the particle becomes 8 3cm / s, will be (a) 2 3cm (b) 3cm (c) 1 cm (d) 2 cm 48. The maximum velocity of a simple harmonic motion represented by       = + 6 3 sin 100  y t is given by (a) 300 (b) 6 3 (c) 100 (d) 6  49. The displacement equation of a particle is x = 3sin2t + 4 cos2t. The amplitude and maximum velocity will be respectively (a) 5, 10 (b) 3, 2 (c) 4, 2 (d) 3, 4 50. Velocity at mean position of a particle executing S.H.M. is v, they velocity of the particle at a distance equal to half of the amplitude (a) 4v (b) 2v (c) v 2 3 (d) v 4 3 51. The instantaneous displacement of a simple pendulum oscillator is given by       = + 4 cos  x A t . Its speed will be maximum at time (a)   4 (b)   2 (c)   (d)  2 52. Which of the following is a necessary and sufficient condition for S.H.M. (a) Constant period (b) Constant acceleration (c) Proportionality between acceleration and displacement from equilibrium position (d) Proportionality between restoring force and displacement from equilibrium position 53. 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 and stops there (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 54. The acceleration of a particle in S.H.M. is (a) Always zero (b) Always constant (c) Maximum at the extreme position (d) Maximum at the equilibrium position 55. The displacement of a particle moving in S.H.M. at any instant is given by y = a sin t . The acceleration after time 4 T t = is (where T is the time period) (a) a (b) −a (c) 2 a (d) 2 − a 56. 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 (a) 2 2 144  m /sec (b) 2 144 m /sec (c) 2 2 / 144 m sec  (d) 2 2 288  m /sec 57. 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 (a) 98.596 N (b) 985.96 N (c) 100.2 N (d) 76.23 N 58. A body executing simple harmonic motion has a maximum acceleration equal to 2 24metres /sec and maximum velocity equal to 16 metres /sec . The amplitude of the simple harmonic motion is (a) metres 3 32 (b) metres 32 3 (c) metres 9 1024 (d) metres 9 64 59. For a particle executing simple harmonic motion, which of the following statements is not correct (a) The total energy of the particle always remains the same (b) The restoring force of always directed towards a fixed point (c) The restoring force is maximum at the extreme positions (d) The acceleration of the particle is maximum at the equilibrium position