Skip to main content

Formula Undamped Harmonic Oscillator Velocity    Amplitude    Time    Angular frequency    Phase

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

Velocity

Unit
Velocity of the harmonic oscillator at the time \(t\). It can be, for example, the velocity of the oscillating mass hanging on a spring.

Amplitude

Unit
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).

Time

Unit
Time at which the velocity is \(v(t)\).

Angular frequency

Unit
Angular frequency \(\omega = 2\pi\,f\) describes how fast the harmonic oscillator oscillates.

Phase

Unit
Phase is an angular quantity that determines what velocity \(v(0)\) the harmonic oscillator had at time \(t=0\):$$ v(0) ~=~ -\omega\,A\,\sin(\varphi) $$