Oscillation Lecture Notes

Dunman High School (Senior High Physics Department) 9646 Physics Topic 9: Oscillations 9-1 H2 Topic 9 Oscillations Do you know why that most grandfather clocks, invented in 1656, will have a pendulum of length ≈1m while smaller versions have a pendulum of length ≈25cm? Do you know that these clocks will ‘slow down’ on top of Mount Everest? These clocks were the most accurate time keepers until quartz was invented in 1927! What is the period of these clocks (1.0m and 0.25m)? A 0.5 s B 1.0 s C 2.0 s D 1 minute

Dunman High School (Senior High Physics Department) 9646 Physics Topic 9: Oscillations 9-2 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) understand 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) recognise and use the equation xa 2ω−= as the defining equation of simple harmonic motion. (e) recall and use txx ωsin0= as a solution to the equation xa 2ω−= . (f) recognise and use )( cos 22 0 0 xxv tvv −±= = ω ω (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 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 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. References: 1 Advanced Level Physics by Loo Kwok Wai 2 College Physics by Young and Geller 3 Physics for Scientist and Engineers (5th Edition) by Serway

Dunman High School (Senior High Physics Department) 9646 Physics Topic 9: Oscillations 9-3 1 Introduction (a) describe simple examples of free oscillations. An oscillation is a periodic motion of an object about a certain mean equilibrium position with a continuous interchange of kinetic energy and potential energy. Periodic (or harmonic) motion refers to any motion that repeats itself in equal intervals of time. Examples: vibration of tuning fork, boat bobbing at anchor, a child playing on a swing,