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Formula Damped Harmonic Oscillator Frequency    Spring constant    Mass    Damping constant

Formula: Damped Harmonic Oscillator
Hooke Law: Displacement of the spring and restoring force
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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

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


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

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