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≤} =
