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Module 5: Newtonian world and astrophysics

5.3 Oscillations

5.3.1

Simple harmonic oscillations

 (a) displacement, amplitude, period, frequency, angular frequency and phase difference

Multiple Choice

Structured

(b) angular frequency ω,

ω =2π/T

or

ω = 2πf

(c) (i) simple harmonic motion;

defining equation:

a = - ω2x

(ii) techniques and procedures used to determine the period/frequency of simple harmonic oscillations

e.g. mass on a spring, pendulum

(d) solutions to the equation

a = - ω2x

e.g. x = A cos ωt or

x = A sin ωt

(e) velocity v = ± ω√(A2 - x2)

hence vmax = ωA

(f) the period of a simple harmonic oscillator is independent of its amplitude (isochronous oscillator)

(g) graphical methods to relate the changes in displacement, velocity and acceleration during simple harmonic motion.

5.3.2

Energy of a simple harmonic oscillator

 (a) interchange between kinetic and potential
energy during simple harmonic motion
    
(b) energy-displacement graphs for a simple
harmonic oscillator		    

5.3.3 Damping

 (a) free and forced oscillations
    
(b) (i) the effects of damping on an oscillatory
system.		    
(ii) observe forced and damped oscillations for
a range of systems		    
(c) resonance; natural frequency    
(d) amplitude-driving frequency graphs for forced oscillators    
(e) practical examples of forced oscillations and
resonance.