After the beginning of motion,how long will i | vedclass

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(C) The particle starts from rest,which means it starts from the extreme position. The displacement equation is given by $x = A \cos(\omega t)$.Given

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$4$

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(C) The particle starts from rest,which means it starts from the extreme position. The displacement equation is given by $x = A \cos(\omega t)$.Given that the displacement $x = \frac{A}{2}$,we have $\frac{A}{2} = A \cos(\omega t)$.This simplifies to $\cos(\omega t) = \frac{1}{2}$.Since $\cos(\frac{\pi}{3}) = \frac{1}{2}$,we have $\omega t = \frac{\pi}{3}$.Substituting $\omega = \frac{2\pi}{T}$,we get $\frac{2\pi}{T} t = \frac{\pi}{3}$.Given $T = 24 \ sec$,we substitute the value: $\frac{2\pi}{24} t = \frac{\pi}{3}$.Solving for $t$: $\frac{\pi}{12} t = \frac{\pi}{3}$,which gives $t = \frac{12}{3} = 4 \ sec$.

After the beginning of motion,how long will it take for a harmonically oscillating particle to reach a displacement equal to one-half of its amplitude,if the time period is $24 \ sec$ and the particle starts from rest?

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