Question

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)

• A.
• B.
• C.
• D.

Answer 1

Answer: (A)

Taking minimum potential energy at mean position to be zero,
the expression of KE and PE are $KE=\frac{1}{2}m \omega;^2(A^2-d^2)$ and $PE=\frac{1}{2}m \omega;^2d^2$
Both graphs are parabola. At $d = 0$,
the mean position $PE = 0$ and $KE=\frac{1}{2}m \omega^2 A^2 $ =maximum
At $d=\pm;A,$ the extreme positions,
$KE = 0$ and $PE=\frac{1}{2}m \omega^2 A^2$ =maximum
Therefore, the correct graph is (a).