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(A) The time period of the oscillation is given as $T = 8 \,s$.In a simple harmonic motion,the potential energy $(PE)$ is given by $U = \frac{1}{2} k

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$2$

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(A) The time period of the oscillation is given as $T = 8 \,s$.In a simple harmonic motion,the potential energy $(PE)$ is given by $U = \frac{1}{2} k x^2$.The potential energy is minimum $(U_{min} = 0)$ at the mean position $(x = 0)$.The potential energy is maximum $(U_{max} = \frac{1}{2} k A^2)$ at the extreme positions $(x = \pm A)$.The particle moves from the mean position $(x = 0)$ to an extreme position $(x = A)$ in a time interval of $\Delta t = \frac{T}{4}$.Substituting the given value of $T = 8 \,s$:$\Delta t = \frac{8 \,s}{4} = 2 \,s$.Therefore,the maximum value of $PE$ is attained $2 \,s$ after attaining its minimum value.

If a particle repeats its motion after a fixed time interval of $8 \,s$,then after how much time will its maximum value of $PE$ be attained after attaining its minimum value?

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