NJC 2023 Oscillations Notes

NATIONAL JUNIOR COLLEGE 1 2023SH1 | Science | Physics © 2023 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 an d retrieval system,without prior permission in writing from the copyright owner. Oscillations (Topic 10) Content 1. Mathematical Pre-requisite 2. Free Oscillation and Simple Harmonic Motion 3. Energy in Simple Harmonic Motion 4. Damped Oscillation 5. Forced Oscillation and Resonance Learning Outcomes Candidates should be able to: (a) describe simple examples of free oscillations. (b) investigate the motion of an oscillator using experimental and graphical methods. (c) Show an understanding of and use the terms amplitude, period, frequency, angular frequency and phase difference and express the period in terms both frequency and angular frequency. (d) recall and use the equation a = −2x as the defining equation of simple harmonic motion. (e) recognise and use x = x0 sin t as a solution to the equation a = −2x. (f) recognise and use the equations v = v0 cos t and 22 0()v x x = − (g) describe, with graphical illustrations, the changes in displacement, velocity and acceleration during simple harmonic motion. (h) describe the interchange between kinetic and potential energy during simple harmonic motion. (i) describe practical examples of damped oscillations with particular reference to the effects of the degree of damping and the importance of critical damping in applications such as a car suspension system. (j) describe practical examples of forced oscillations and resonance. (k) describe graphically how the amplitude of a forced oscillation changes with frequency near to the natural frequency of the system, and understand qualitatively the factors which determine the frequency response and sharpness of the resonance. (l) show an appreciation that there are some circumstances in which resonance is useful and other circumstances in which resonance should be avoided. Important Note: For this topic your calculator needs to be in radian mode. Otherwise there will be calculation errors.

NATIONAL JUNIOR COLLEGE 2 2023SH1 | Science | Physics © 2023 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 an d retrieval system,without prior permission in writing from the copyright owner. 1. Mathematical Pre-requisite In this chapter, you will use the sine (sinusoidal) graph frequently and hence, you need to know how to sketch the sine graph given an equation of the form 𝑥 = 𝑥0 sin 𝜃 as shown in Fig. 1A below: Notice that the sine graph repeats itself after every 2 radians or 360