# Applications of Harmonic Motion

## Contents

#### Terms

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

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

 Equation for angular displacement of a torsional oscillator θ = θ mcos(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 = x m e cos(σ â≤ t)

 Equation for the angular frequency of a damped system σ â≤ =