Applications of Harmonic Motion
Terms and Formulae
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≤ = 
|
