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(A) The displacement equation is $x = A \sin (2\pi t + \pi /3).$Velocity $v$ is given by the derivative of displacement with respect to time: $v = \fr

Vedclass · Accepted Answer

$0.33$

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(A) The displacement equation is $x = A \sin (2\pi t + \pi /3).$Velocity $v$ is given by the derivative of displacement with respect to time: $v = \frac{dx}{dt} = A(2\pi) \cos (2\pi t + \pi /3).$Velocity is maximum when the magnitude of the cosine term is maximum,which occurs at the mean position where $x = 0$.Setting $x = 0$,we get $\sin (2\pi t + \pi /3) = 0$.This implies the argument $(2\pi t + \pi /3) = n\pi$,where $n$ is an integer.For $n = 0$,$2\pi t = -\pi /3$,which gives $t For $n = 1$,$2\pi t + \pi /3 = \pi$.$2\pi t = \pi - \pi /3 = 2\pi /3$.$t = 1/3 \approx 0.33 	ext{ s}$.Thus,the first time after $t = 0$ when the velocity is maximum is $0.33 	ext{ s}$.

The displacement of a body executing $SHM$ is given by $x = A \sin (2\pi t + \pi /3).$ The first time from $t = 0$ when the velocity is maximum is .... $\sec$

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