Equation of Simple Harmonic Motion – Rankers Physics
Topic: Oscillation
Subtopic: Equation of SHM

Equation of Simple Harmonic Motion

Equation of SHM of a particle whose amplitude is 0.1 m and frequency is 25 Hz with an initial phase of \(\frac{\pi}{4}\) radians is
\(x = 0.1 sin \left(2\pi t + \frac{\pi}{4}\right)\)
\(x = 0.1 sin \left(2\pi t - \frac{\pi}{4}\right)\)
\(x = 0.1 sin \left(50\pi t + \frac{\pi}{4}\right)\)
\(x = 0.1 sin (50\pi t)\)

Solution:

Using standard SHM formula \(x = A sin(\omega t + phi)\), where \(A = 0.1 \text{m}\), \(\omega = 2\pi f = 2\pi(25) = 50\pi \text{rad/s}\), and \(\phi = \frac{\pi}{4}\). Substituting gives \(x = 0.1 sin \left(50\pi t + \frac{\pi}{4}\right)\).

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