DHS 08 Oscillations (Lecture Notes & Tutorial)

Dunman High School (Senior High Physics) - Oscillations DHS Y5 Physics H2 (2023) For Internal Use Only Page 1 of 34 Topic 10 Oscillations Guiding Questions • What are the characteristics of periodic motion? How can we study and describe such motion? • How can circular motion be related to simple harmonic motion? • How do we analyse simple harmonic motion? Content • Simple harmonic motion • Energy in simple harmonic motion • Damped and forced oscillations, 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 of both frequency and angular frequency (d) recall and use the equation as the defining equation of simple harmonic motion (e) recognise and use as a solution to the equation (f) recognise and use the equations and (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 to the importance of critical damping in cases 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 driving frequency near to the natural frequency of the system, and understand qualitatively the factors which determine the frequency response and the 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. 2ax =− 0 sinx x t = 2ax =− 0 cosv v t = ( ) 22 0v x x= −

Dunman High School (Senior High Physics) - Oscillations DHS Y5 Physics H2 (2023) For Internal Use Only Page 2 of 34 Introduction An oscillation is a periodic to-and-fro motion of an object between two limits. Periodic means the oscillations repeat themselves. There are three types of oscillations: (1) free oscillation, (2) damped oscillation, & (3) forced oscillation (a) describe simple examples of free oscillations Free Oscillations (oscillating system is isolated) When an object undergoes free oscillation, it oscillates with no energy gain or loss . The object oscillates with constant amplitude, as there are no external force acting on it. Examples of free oscillations include, when friction and air resistance are negligible, (1) a simple vertical (vibrating) spring-mass system, (2) a simple horizontal spring-mass system, and (3) a simple (swinging) pendulum It can be show