Title 11-simple-harmonic-motion-.pdf ✅

Simple Harmonic Motion 1. A body executing SHM on a straight line ABC has extreme position at points A and C, such that AB = a and BC = b. The velocity of particle at mid point of line ABC is u. The time period of SHM is : (A) 2π(b−a) u (B) π(b−a) u (C) π(a+b) u (D) 2π(a+b) u 2. A spring has an equilibrium length of 2.0 meters and a spring constant of 10 N/m. Alice is pulling on one end of the spring with a force 3.0 N. Bob is pulling on the opposite end of the spring with a force of 3.0 N, in the opposite direction. What is the resulting length of the spring? (A) 1.7 m (B) 2.0 m (C) 2.3 m (D) 2.6 m 3. An object of mass 0.2 kg executes simple harmonic oscillations along X-axis with a frequency of (25/π) Hz. At the position x = 0.04 m, the object has kinetic energy of 0.5 J and potential energy of 0.4 J. Find the amplitude of oscillations (in cm ). [assume zero potential energy at equilibrium position] (A) 2 cm (B) 4 cm (C) 5 cm (D) 6 cm 4. The displacement of a particle varies with time according to the relation : y = asin ωt + bcos ωt (A) The motion is oscillatory but not S.H.M. (B) The motion is S.H.M. with amplitude a + b (C) The motion is S.H.M. with amplitude a 2 + b 2 (D) The motion is S.H.M. with amplitude √a 2 + b 2 5. The equation of motion of a particle is x = acos (αt) 2 . The motion is : (A) periodic but not oscillatory (B) periodic and oscillatory (C) oscillatory but not periodic (D) neither periodic nor oscillatory 6. When a mass m is connected individually to two springs S1 and S2 the oscillation frequencies are v1 and v2. If the same mass is attached to the springs as shown in figure, the oscillation frequency would be : (A) v1 + v2 (B) √v1 2 + v2 2 (C) ( 1 v1 + 1 v2 ) −1 (D) √v1 2 − v2 2 7. A particle executing a simple harmonic motion has a period of 6 s. The time taken by the particle to move from the position of half the amplitude, starting from the mean position is : (A) 1/4s (B) 3/4s (C) 1/2s (D) 3/2s 8. The speed of propagation of a wave in a medium is 300 m/s −1 . The equation of motion of point at x = 0 is given y = 0.04sin 600πt (meter). The displacement of a point x = 75 cm at t = 0.01 s is: (A) 0.02 m (B) 0.04 m (C) Zero (D) 0.028 m 9. Consider the following statements : The total energy of a particle executing simple harmonic motion depends on its I. amplitude II. period III. displacement (A) I and II are correct (B) II and III are correct (C) I and III are correct (D) I, II and III are correct 10. The equation of a simple harmonic progressive wave is given by y = Asin (100πt − 3x). Find the distance between 2 particles having a phase
difference of π/3. (A) π/9m (B) π/18 m (C) π/6 m (D) π/3 m 11. y = 3sin π ( t 2 − x 4 ) represents an equation of a progressive wave, where t is in second and x is in meter. The distance travelled by the wave in 5s is : (A) 8 m (B) 10 m (C) 5 m (D) 32m PARAGRAPH FOR QUESTIONS 12 - 14 Incident wave y = Asin (ax + bt + π 2 ) is reflected by an obstacle at x = 0 which reduces intensity of reflected wave by 36%. Due to superposition a resulting wave consist of standing wave and traveling y = −1.6Asin axsin bt + cAcos (bt + ax) where A, ab and c are positive constants. 12. Amplitude of reflected wave is : (A) 0.6A (B) 0.8 A (C) 0.4A (D) 0.2A 13. Value of c is : (A) 0.2 (B) 0.4 (C) 0.6 (D) 0.3 14. Position of second antinode is : (A) x = π 3a (B) x = 3π a (C) x = 3π 2a (D) x = 2π 3a 15. Find time period of oscillation for arrangement shown in figure. (A) 2π√ m 2k (B) 2π√ 2m k (C) π√ m k (D) π√ m 2k (D) 1 2π √( 4k m ) 16. A mass is m is attached to four springs of spring constants 2k, 2k, k, k as shown in figure. The mass is capable of oscillating on a frictionless horizontal floor. If it is displaced slightly and released the frequency of resulting SHM would be : (A) 1 2π √( 11k 2m ) (B) 1 2π √( 2k 3m ) (C) 1 2π √( 3k m ) (D) parabola 17. The graph between the time period and the length of a simple pendulum is : (A) straight line (B) curve (C) ellipse (D) parabola 18. A flat plate P of mass M executes S.H.M. on a horizontal plane by sliding over a frictionless surface with a frequency v. A block B of mass m rests on the plate as shown in figure. Coefficient of friction between the surfaces of B and P is μs . If the block B is not to slip on the plate, then the maximum amplitude of oscillation that the plate block system can have is: (A) μg 4πv 2 (B) μ 2g π2v 2 (C) μ 2g 4π2v 2

(A) 10.5 Hz (B) 105 Hz (C) 155 Hz (D) 205 Hz 25. A particle executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. Then, its time period of vibration will be : (A) β 2 α (B) 2πβ α (C) β 2 α2 (D) α β 26. A particle is executing SHM along a straight line. Its velocities at distances x1 and x2 from the mean position are V1 and V2, respectively. Its time period is : (A) 2π√ V1 2+V2 2 x1 2+x2 2 (B) 2π√ V1 2−V2 2 x1 2−x2 2 (C) 2π√ x1 2+x2 2 V1 2+V2 2 (D) 2π√ x2 2−x1 2 V1 2−V2 2 27. When two displacement represented by y1 = asin (ωt) and y2 = bcos (ωt) are superimposed the motion is : (A) simple harmonic with amplitude √a 2 + b 2 (B) simple harmonic with amplitude (a 2+b 2 ) 2 (C) not a simple harmonic (D) simple harmonic with amplitude a b 28. The oscillation of a body on a smooth horizontal surface is represented by the equation, X = Acos (ωt); where X = displacement at time t and ω = frequency of oscillation. Which one of the following graphs shows correctly the variation a with t ? (A) (B) (C) (D) Here a = acceleration at time t and T = time period 29. Out of the following functions representing motion of a particle which represents SHM : I. y = sin ωt − cos ωt II. y = sin3 ωt III. y = 5cos ( 3π 4 − 3ωt) IV. y = 1 + ωt + ω 2 t 2 The correct choice is : (A) Only I (B) Only IV does not represent SHM (C) Only I and III (D) Only I and II 30. Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is : (A) π 6 (B) 0