Oscillations Simple Harmonics

Oscillations An oscillation is any movement that involves repetitive to- and-fro motion. One complete movement from the starting position, to a second position and back to the starting position is an oscillation. Pendulum Beating heart Child on a swing Vibrations on instrument strings Ball bouncing up and down Springs

Frequency is measured in hertz (Hz) One hertz is one oscillation per second (1 Hz = 1 s^-1) Frequency f = 1/T Displacement – the distance from the equilibrium position Amplitude – the maximum displacement

Displacement-time graphs For most oscillations the graph resembles a sine or cosine curve. These type of oscillations are know as Simple harmonic motions (s.h.m)

Simple Harmonic Motion

Simple Harmonic Motion Why the negative sign? This is because the negative sign tells us the acceleration a is always in the opposite direction to the displacement x. Acceleration is always directed towards the point where displacement is measured

Angular Frequency ω Angular frequency ω is related to the frequency f of the oscillation by the expression

Solution of equation for s.h.m To find the displacement – time relation for a particle moving in a s.h.m you have to solve the equation 𝑎=− ω 2 𝑥. To derive this equation requires math beyond this course, for the form is

The Velocity curve is π/2 rad ahead of the displacement curve.

Maximum Speed

Equation for the acceleration

Example

Classwork