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

Formula
Formula: Sinusoidally Forced Damped Oscillator
Amplitude-Frequency Graph of a Forced Damped Oscillator

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.