# Formula Damped Harmonic Oscillator Frequency Spring constant Mass Damping constant

## Frequency

`$$ f $$`Unit

`$$ \mathrm{Hz} = \frac{ 1 }{ \mathrm{s} } $$`

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

`$$ D $$`Unit

`$$ \frac{\mathrm N}{\mathrm m} $$`

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

## Mass

`$$ \class{brown}{m} $$`Unit

`$$ \mathrm{kg} $$`

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

`$$ b $$`Unit

`$$ \frac{\mathrm{kg}}{\mathrm s} $$`

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:`$$ f ~=~ \frac{1}{2\pi} \sqrt{\frac{D}{m}} $$`