TJC 9 Oscillations notes

i Unit 9: Oscillations Learning Outcomes Candidates should be able to: (a) describe simple examples of free oscillations, where particles periodically return to an equilibrium position without gaining energy from or losing energy to the environment (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, phase and phase difference and express the period in terms of both frequency and angular frequency (d) show an understanding that a =  2x is the defining equation of simple harmonic motion, where acceleration is (directly) proportional to displacement from an equilibrium position and acceleration is always directed towards the equilibrium position (e) recognise and use x = xo sint as a solution to the equation a =  2x (f) recognise and use the equations v = vo cost and 2 2 ov x x    (g) describe, with graphical illustrations, the relationships between 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 to the importance of critical damping in applications such as a car suspension system (j) describe graphically how the amplitude of a forced oscillation changes with driving frequency, resulting in maximum amplitude at resonance when the driving frequency is close to or at the natural frequency* of the system (k) show a qualitative understanding of the effects of damping on the frequency response and sharpness of the resonance (l) describe practical examples of forced oscillations and resonance, and show an appreciation that there are some circumstances in which resonance is useful, and other circumstances in which resonance should be avoided *Natural frequency refers to the frequency when the system is in free oscillation. Temasek Junior College 2025 Name : ________________________________ Class : _________

2 1 Introduction An oscillation is a motion in which a system moves to-and-fro along the same path repeatedly. The oscillation of a pendulum of a clock is apparent, but the oscillation of atoms within a solid is hidden. The oscillation associated with wave motion can be appreciated when a body floating in a liquid rises and falls as a wave travels past it, but the oscillation associated with light waves cannot be perceived by our senses. In fact, all communication by sight and by hearing makes use of wave oscillation. 1.1 Free oscillations LO (a) In a free oscillation, the particle periodically returns to an equilibrium position without gaining energy from or losing energy to the environment. The only external force acting on it is the restoring force and it oscillate