Review of Oscillations
Terms and Formulae
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 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 = x mcos(σt) |
| Equation for the velocity in simple harmonic motion | v = σx msin(σt) |
| Equation for the acceleration in simple harmonic motion | a = σ 2 x mcos(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 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≤ = 
|
