# Oscillations and Simple Harmonic Motion

## Contents

#### Terms

Oscillating system  -  Any system that always experiences a force acting against the displacement of the system (restoring force).
Restoring force  -  A force that always acts against the displacement of the system.
Periodic Motion  -  Any motion in which a system returns to its initial position at a later time.
Amplitude  -  The maximum displacement of an oscillating system.
Period  -  The time it takes for a system to complete one oscillation.
Frequency  -  The rate at which a system completes an oscillation.
Hertz  -  The unit of measurement of frequency.
Angular Frequency  -  The radian measure of frequency: frequency times 2Π .
Simple Harmonic Motion  -  Any motion that experiences a restoring force proportional to the displacement of the system.

#### Formulae

 Relation between variables of oscillation σ = 2Πν =

 Force exerted by a spring with constant k F = - kx

 Differential equation describing simple harmonic motion + x = 0

 Formula for the period of a mass-spring system T = 2Π

 Formula for the frequency of a mass-spring system ν =

 Formula for the angular frequency of a mass-spring system σ =

 Equation for the displacement in simple harmonic motion x = x mcos(σt)

 Equation for the velocity in simple harmonic motion v = σx msin(σt)

 Equation for the acceleration in simple harmonic motion a = σ 2 x mcos(σt)

 Equation for the potential energy of a simple harmonic system U = kx 2