All about waves

Page
3

Slide 22

Simple Harmonic Motion1

Period is independent of amplitude

Same time for a large swing and a small swing

For a pendulum this only works for angles of deflection up to about 20º

Slide 23

SHM2

Gradient of displacement v. time graph gives a velocity v. time graph

Max veloc at x = 0

Zero veloc at x = max

Slide 24

SHM3

Acceleration v. time graph is produced from the gradient of a velocity v. time graph

Max a at V = zero

Zero a at v = max

Slide 25

SHM4

Displacement and acceleration are out of phase

a is proportional to - x

Hence the minus

Slide 26

SHM5

a = -ω²x equation defines SHM

T = 2π/ω

F = -kx eg a trolley tethered between two springs

Slide 27

Circular Motion and SHM

The peg following a circular path casts a shadow which follows SHM

This gives a mathematical connection between the period T and the angular velocity of the rotating peg

T = 2π/ω