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Applications of Harmonic Motion

Terms and Formulae

Introduction and Summary

Applications of Simple Harmonic Motion

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≤ =

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