1. Oscillations
Simple Harmonics

2. 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

4. 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

5. 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)

6. Simple Harmonic Motion

7. 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

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

9. 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

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

13. Maximum Speed

14. Equation for the acceleration

15. Example

17. Classwork