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

1. Energy at the Mean Position ($$d = 0$$):

At the center of the oscillation (mean position), the pendulum bob has its maximum velocity. Therefore, Kinetic Energy is maximum and Potential Energy is minimum and equal to zero.

2. Energy at the Extreme Positions ($$d = \pm A$$):

At the maximum displacement (amplitude), the bob momentarily comes to rest before changing direction. Therefore, Kinetic Energy is zero and Potential Energy is maximum.

$$P.E. = \frac{1}{2}m\omega^2 d^2$$  (This is the equation of a parabola opening upwards with its vertex at the origin)

$$K.E. = \frac{1}{2}m\omega^2 (A^2 - d^2)$$ (This is the equation of a parabola opening downwards with its maximum value at $$d = 0$$)

The total energy $$E = K.E. + P.E. = \frac{1}{2}m\omega^2 A^2$$ remains constant throughout the motion.

Based on all these, option (C) represents the graph most accurately.