• ### 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 = xme cos(σâ≤t)

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