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Formula Undamped Harmonic Oscillator Acceleration    Amplitude    Time    Angular frequency    Phase

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

Unit
Acceleration of the harmonic oscillator at the time \(t\). This can be, for example, the acceleration 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 acceleration is \(a(t)\).

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 acceleration \(a(0)\) the harmonic oscillator had at time \(t=0\):$$ a(0) ~=~ -\omega^2\,A\,\cos(\varphi) $$