###
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 2*Π*.

**
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* = 2*Πν* = |

**
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* = 2*Π* |

**
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*_{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* = 2*Π* |

**
Equation for the angular frequency of a torsional oscillator
** | *σ* = |

**
Equation for the force felt by a pendulum
** | *F* = *mg* sin*θ* |

**
Approximation of the force felt by a pendulum
** | *F* - ()*x* |

**
Equation for the period of a pendulum
** | *T* = 2*Π* |

**
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≤} = |