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(D) For a simple harmonic oscillator,the potential energy $(PE)$ is given by $PE = \frac{1}{2} k d^2$,where $k$ is the force constant and $d$ is the d

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(D) For a simple harmonic oscillator,the potential energy $(PE)$ is given by $PE = \frac{1}{2} k d^2$,where $k$ is the force constant and $d$ is the displacement. This represents a parabola opening upwards with its vertex at the origin $(0,0)$.The kinetic energy $(KE)$ is given by $KE = \frac{1}{2} k (A^2 - d^2)$,where $A$ is the amplitude. This represents a downward-opening parabola with its maximum value at the mean position $(d=0)$ and zero at the extreme positions $(d = \pm A)$.Comparing these with the given options,the graph that shows $PE$ as an upward-opening parabola starting from the origin and $KE$ as a downward-opening parabola with its maximum at the origin is represented by the graph in option $D$.

For a simple pendulum,a graph is plotted between its kinetic energy $(KE)$ and potential energy $(PE)$ against its displacement $d$. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)

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