Skip to main content

Formula Undamped Harmonic Oscillator Velocity    Current position    Mass    Spring constant    Amplitude

Formula: Undamped Harmonic Oscillator
Hooke Law: Displacement of the spring and restoring force
Hover the image! Get this illustration


Velocity \(v(x)\) of an undamped harmonic oscillator as a function of its current position \(x\). For example, its velocity is zero at the maximum deflection \(A\):$$ v(A) ~=~ \sqrt{ \frac{D}{m} \, \left(A^2 - A^2\right) } ~=~ 0 $$

Current position

Current position of a harmonic oscillator at which it has the velocity \(v(x)\). For example, it could be the current deflection of the spring on which a mass is attached.


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.


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 (undeflected mass).