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Formula Undamped Harmonic Oscillator Maximum velocity    Amplitude    Mass    Spring constant

Formula: Undamped Harmonic Oscillator
Hooke Law: Displacement of the spring and restoring force
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Maximum velocity

Maximum velocity that can occur in a harmonic oscillation. For a spring pendulum, it is the maximum velocity of the mass connected to a spring. Here \(\omega = \sqrt{ \frac{D}{m} }\) is the angular frequency:$$ v_{\text{max}} ~=~ \omega \, A $$


Maximum deflection of a harmonic oscillator. In the case of a spring pendulum, it is the maximum distance of the mass from the rest position of the spring (undeflected mass).


Mass of the 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 taken into account in \(m\) because it also oscillates.

Spring constant

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