What is the maximum velocity of a simple harm | vedclass

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(D) The displacement of a particle in simple harmonic motion is given by $x = a \sin(\omega t + \phi)$.The velocity $v$ is the derivative of displacem

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$\frac{2\pi a}{T}$

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(D) The displacement of a particle in simple harmonic motion is given by $x = a \sin(\omega t + \phi)$.The velocity $v$ is the derivative of displacement with respect to time: $v = \frac{dx}{dt} = a\omega \cos(\omega t + \phi)$.The maximum velocity $V_{max}$ occurs when $\cos(\omega t + \phi) = 1$,so $V_{max} = a\omega$.Since the angular frequency $\omega = \frac{2\pi}{T}$,substituting this into the expression gives $V_{max} = a \left(\frac{2\pi}{T}\right) = \frac{2\pi a}{T}$.

What is the maximum velocity of a simple harmonic motion with amplitude '$a$' and time period '$T$ seconds'?

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