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)

Answer 2

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