# Formula Sinusoidally Forced Damped Oscillator Amplitude    Force    Excitation frequency    Natural frequency    Mass    Damping constant

## Amplitude

Unit
The maximum displacement of a forced damped oscillation.

## Force

Unit
Amplitude of an external sinusoidal force with which the oscillator is excited:$$F_{\text{ext}} ~=~ F_0 \, \cos(\omega\,t)$$

Here $$t$$ is the time.

## Excitation frequency

Unit
Excitation frequency of an external sinusoidal force:$$F_{\text{ext}} ~=~ F_0 \, \cos(\omega\,t)$$

## Natural frequency

Unit
Frequency at which the oscillator oscillates when it is made to oscillate once.

## Mass

Unit
Mass of the damped oscillator. For a spring pendulum, it is in good approximation the mass hanging on the spring. In the case of a spring whose mass cannot be neglected, a part of the mass of the spring must also be taken into account in $$m$$ because it also oscillates.

## Damping constant

Unit
The damping constant is a measure of how fast the oscillations decay. Depending on the value of the damping constant, we get a underdamped, critically damped or overdamped oscillator.