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(D) The equation of motion is given by $x = 5 \sin \left( 4t - \frac{\pi}{6} \right)$.Comparing this with the standard equation $x = A \sin(\omega t +

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$16$

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(D) The equation of motion is given by $x = 5 \sin \left( 4t - \frac{\pi}{6} ight)$.Comparing this with the standard equation $x = A \sin(\omega t + \phi)$,we get the amplitude $A = 5$ and the angular frequency $\omega = 4$.The velocity $v$ of a particle in simple harmonic motion at a displacement $x$ is given by the formula $v = \omega \sqrt{A^2 - x^2}$.Substituting the given values $A = 5$,$\omega = 4$,and $x = 3$:$v = 4 \sqrt{5^2 - 3^2}$$v = 4 \sqrt{25 - 9}$$v = 4 \sqrt{16}$$v = 4 	imes 4 = 16$ units.

$A$ particle is in simple harmonic motion. The equation of its motion is $x = 5 \sin \left( 4t - \frac{\pi}{6} \right)$,where $x$ is its displacement. If the displacement of the particle is $3$ units,then its velocity is:

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