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

Maximum Speed in Simple Harmonic Motion

If \( x = 2\sin\left(\frac{\pi}{2}t\right) \) represents the motion of a particle executing SHM, the maximum speed of the particle in \( \text{m s}^{-1} \) is (All parameters are in SI units)
\( \frac{\pi}{2} \)
\( 2\pi \)
\( \frac{2\pi}{3} \)
\( \pi \)

Solution:

Comparing the given equation with the standard SHM equation \( x = A\sin(\omega t) \), we get \( A = 2\text{ m} \) and \( \omega = \frac{\pi}{2}\text{ rad/s} \). The maximum speed is \( v_{\max} = A\omega = 2 \times \frac{\pi}{2} = \pi\text{ m/s} \).

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