Skip to main content

Formula Sinusoidally Forced, Damped Oscillator Phase angle    Mass    Damping constant    Natural frequency    Anregungsfrequenz

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

Phase angle

Unit
Phase constant \(\varphi_0\) of sinusoidally forced damped oscillation indicates the displacement \(y(t)\) at time \(t=0\):$$ y(0) ~=~ A_0 \, \cos(\varphi_0) $$

Mass

Unit
Mass of the forced, damped oscillator. For a spring pendulum, it is, to a good approximation, the mass attached to the spring.

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.

Natural frequency

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

Anregungsfrequenz

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