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 massspring system
 T = 2Π 
Formula for the frequency of a massspring system
 ν = 
Formula for the angular frequency of a massspring system
 σ = 
Equation for the displacement in simple harmonic motion
 x = x_{m}cos(σt) 
Equation for the velocity in simple harmonic motion
 v = σx_{m}sin(σt) 
Equation for the acceleration in simple harmonic motion
 a = σ^{2}x_{m}cos(σt) 
Equation for the potential
energy of a
simple
harmonic system
 U = kx^{2} 
Equation for the torque felt in a torsional oscillator
 τ =  κσ 
Equation for angular displacement of a torsional oscillator
 θ = θ_{m}cos(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≤} = 