Oscillations & Fields

PH4.1 BASIC PHYSICS

Content

• Circular motion
• Physical and mathematical treatment of undamped simple harmonic

motion.

• Energy interchanges during simple harmonic motion.
• Damping of oscillations.
• Free oscillations, forced oscillations and resonance.

AMPLIFICATION OF CONTENT Candidates should be able to:

4.1 (a) understand and use period of rotation, frequency, the radian measure of angle,

4.1 (b) define and use angular velocity ω ,

4.1 (c) recall and use v =ωr, and hence a =ω 2r,

4.1 (d) define simple harmonic motion as a statement in words,

4.1 (e) recall, recognise and use a = −ω 2 x as a mathematical defining equation of simple harmonic motion,

4.1 (f) illustrate, and interpret graphically, the variation of acceleration with displacement during simple harmonic motion,

4.1 (g) recall and use x = Asin(ω t +ε ) as a solution to a = −ω 2 x ,

4.1 (h) explain the terms frequency, period, amplitude and phase (ω t +ε ) ,

4.1 (i) recall and use the period asω 2π 1 or f ,

4.1 (j) recall and use v = Aω cos (ω t +ε ) for the velocity during simple harmonic motion,

4.1 (k) illustrate, and interpret graphically, the changes in displacement and velocity with time during simple harmonic motion,

4.1 (l) recall and use the equation k T = 2π m for the period of a system having stiffness (force per unit extension) k and mass m,

4.1 (m) illustrate, and interpret graphically, the interchange between kinetic energy and potential energy during undamped simple harmonic motion, and perform simple calculations on energy changes,

4.1 (n) explain what is meant by free oscillations and understand the effect of damping in real systems,

4.1 (o) describe practical examples of damped oscillations, and the importance of critical damping in appropriate cases such as vehicle suspensions,

4.1 (p) explain what is meant by forced oscillations and resonance, and describe practical examples,

4.1 (q) sketch the variation of the amplitude of a forced oscillation with driving frequency and know that increased damping broadens the resonance curve,

4.1 (r) appreciate that there are circumstances when resonance is useful e.g. circuit tuning, microwave cooking and other circumstances in which it should be avoided e.g. bridge design.