# Review of Oscillations

### 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.
Torsional Oscillator  -  The oscillation of any object suspended by a wire and rotating about the axis of the wire.
Pendulum  -  The classic pendulum consists of a particle suspended from a light cord. When the particle is pulled to one side and released, it swings back past the equilibrium point and oscillates between two maximum angular displacements.
Damping force  -  A force proportional to the velocity of the object that causes it to slow down.
Resonance  -  The phenomena in which a driving force causes a rapid increase in the amplitude of oscillation of a system.
Resonant Frequency  -  The frequency at which a driving force will produce resonance in a given oscillating 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 = xmcos(σt)

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

 Equation for the acceleration in simple harmonic motion a = σ2xmcos(σt)

 Equation for the potential energy of a simple harmonic system U = kx2

 Equation for the torque felt in a torsional oscillator τ = - κσ

 Equation for angular displacement of a torsional oscillator θ = θmcos(σt)

 Equation for the period of a torsional oscillator T = 2Π

 Equation for the angular frequency of a torsional oscillator σ =

 Equation for the force felt by a pendulum F = mg sinθ

 Approximation of the force felt by a pendulum F - ()x

 Equation for the period of a pendulum T = 2Π

 Differential equation describing damped motion kx + b + m = 0

 Equation for the displacement of a damped system x = xmecos(σâ≤t)

 Equation for the angular frequency of a damped system σâ≤ =