Amplitude of a harmonic oscillator – Rankers Physics
Topic: Oscillation
Subtopic: Equation of SHM

Amplitude of a harmonic oscillator

The displacement of a harmonic oscillator is given by \(x = \alpha \sin\omega t + \beta \cos\omega t\). The amplitude of the oscillation is
\(\alpha + \beta\)
\(\alpha^2 + \beta^2\)
\(\sqrt{\alpha^2 + \beta^2}\)
\(\sqrt{\alpha^2 + \beta^2 + 2\alpha\beta}\)

Solution:

The expression represents two perpendicular SHMs of the same frequency with a phase difference of \(\frac{\pi}{2}\). The resultant amplitude is \(A = \sqrt{\alpha^2 + \beta^2}\).

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