Harmonic Oscillator - Universal Oscillator Equation

The equation

is known as the universal oscillator equation since all second order linear oscillatory systems can be reduced to this form. This is done through nondimensionalization.

If the forcing function is f(t) = cos(ωt) = cos(ωtcτ) = cos(ωτ), where ω = ωtc, the equation becomes

The solution to this differential equation contains two parts, the "transient" and the "steady state".

Read more about this topic:  Harmonic Oscillator

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