NJC 2023 Oscillations Problem Set

NATIONAL JUNIOR COLLEGE 1 2022 | Science | Physics © 2022 National Junior College All Rights Reserved. No part of this publication may be produced or transmitted in any form or by any means, electronic or me chanical, including photocopy,recording or any other information storage and retrieval system, without prior permission in writing from the copyright owner. Oscillations Problem Set Exercises Free Oscillations E1. The displacement x (in metres) of a body in oscillatory motion is given by the equation: x = 3.5 sin 4.0 t (a) Determine the amplitude of the motion. (b) Determine the angular frequency. (c) Determine the displacement 0.20 s after oscillation is begun. [ 2.5 m ] (d) Find the expression of velocity in terms of time and, [v = 14 cos 4.0t ] (e) Hence determine the velocity at time t = 0.50 s. [ -5.8 m s-1 ] E2. [N06/1/13] A simple harmonic oscillator has a time period of 10 seconds. Which equation relates its acceleration a and displacement x? A a = -(20/2π)2x B a = -(20π)2x C a = -(20/2π)x D a = -(2π/10)2x Ans: [D] E3. [N08/1/15] The def ining equation for a particle moving in simple harmonic motion 𝑎 = −𝜔2𝑥 where 𝑎 is the acceleration of the particle, 𝑥 is the displacement and is the angular frequency. The graph on the right shows how 𝑎 varies with 𝑥 for a particle moving in simple harmonic motion. Which is the amplitude and period of the motion? Amplitude/cm Period/s A 5.0 0.44 B 5.0 14 C 10 0.44 D 10 14 Ans: [A]

NATIONAL JUNIOR COLLEGE 2 2022 | Science | Physics © 2022 National Junior College All Rights Reserved. No part of this publication may be produced or transmitted in any form or by any means, electronic or me chanical, including photocopy,recording or any other information storage and retrieval system, without prior permission in writing from the copyright owner. E4. A body performs simple harmonic motion with period of 0.063 s. The maximum speed is 3.0 ms-1. What are the values of the amplitude x0 and the angular frequency ? x0/m /rads-1 A 0.030 100 B 0.19 16 C 5.3 16 D 33 100 Ans: [A] E5. An oscillating system performs s.h.m. with an amplitude of 2.0 cm. If the period of the motion is 5.0 s, calculate (a) the magnitude of the velocity of the particle at 0.50 cm from equilibrium position. [2.43 cm s-1] (b) the maximum acceleration of the particle. [3.16 cm s-2] E6. An object moving with simple harmonic motion has an amplitude of 0.020 m and a frequency of 20 Hz. Calculate (a) the period of oscillation. [0.050 s] (b) the velocity at the equilibrium point and at the position of maximum negative displacement. [2.51 m s-1, 0 m s-1] E7. The motion of a piston in a certain car engine is approximately simple harmonic with amplitude 40 mm. The frequency of oscillation is 120 Hz. Determine (a) the ma