For a simple pendulum, having time period T, | vedclass

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(D) The kinetic energy $(K.E)$ of a simple pendulum is given by $K.E = \frac{1}{2} m v^2$.The velocity $v$ of a simple pendulum performing simple harm

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(D) The kinetic energy $(K.E)$ of a simple pendulum is given by $K.E = \frac{1}{2} m v^2$.The velocity $v$ of a simple pendulum performing simple harmonic motion $(SHM)$ is $v = A\omega \cos(\omega t + \phi)$.Thus, $K.E = \frac{1}{2} m A^2 \omega^2 \cos^2(\omega t + \phi)$.Since $K.E \propto \cos^2(\omega t)$, the graph is a periodic function with a frequency double that of the pendulum's motion, meaning it completes two cycles in the time the pendulum completes one cycle $(T)$.At the mean position $(t=0)$, the velocity is maximum, so kinetic energy is maximum. The graph that shows maximum kinetic energy at $t=0$ and completes two cycles in time $T$ is Graph $D$.

For a simple pendulum, having time period $T$, the variation of kinetic energy $(K.E)$ with time $(t)$ is represented by:

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