# Formula Damped Harmonic Oscillator Frequency    Spring constant    Mass    Damping constant

## Frequency

Unit
Frequency indicates how fast the damped harmonic oscillator oscillates. For example, how fast a mass hanging on a spring oscillates. Unlike an undamped oscillation, the frequency of a damped oscillation is lower because of the factor $$\frac{b^2}{4m^2}$$.

## Spring constant

Unit
Spring constant describes the stiffness of a spring, i.e. how well the spring can be deflected.

## Mass

Unit
Mass of the damped harmonic 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 considered 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.

When the damping constant $$b=0$$ vanishes, we get the frequency of an undamped harmonic oscillator:$$f ~=~ \frac{1}{2\pi} \sqrt{\frac{D}{m}}$$