RI Chap 9 Oscillations Lecture Notes

9 Oscillations H2 Physics 9478 Content Page 9.1 Introduction to Oscillations 2 9.2 Simple Harmonic Motion 4 9.3 Energy in Simple Harmonic Motion 16 9.4 Damped Oscillations 19 9.5 Forced Oscillations and Resonance 23 9.6 Summary of S.H.M Equations 27 9.7 Appendix 28 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 2ax =− 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 0 sinx x t = as a solution to the equation 2ax =− . (f) recognise and use the equations 0 cosv v t = and ( ) 22 0v 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 (light/under, critical, heavy/over), 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 (natural frequency refers to the frequency when the system is in free oscillation). (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.

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT P a g e | 2 9.1 Introduction to Oscillations A periodic motion is one in which a body continually retraces its path at equal time intervals. Many systems exhibit periodic motion. The molecules in a solid oscillate about their equilibrium positions; electromagnetic waves are characterised by oscillating electric and magnetic field vectors; and in alternating -current electrical c ircuits, voltage and current vary periodically with time. An oscillation is a special periodic motion in which the oscillator moves to and fro about an equilibrium position. This is also ca