The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement (x) starting from mean position to extreme position (A) is given by

Solution

Physics sir · 4 steps

Write KE in terms of x first; the formula tells you where the graph starts, ends and bends.

1. Write KE. In SHM the total energy 1/2kA² stays fixed, and the potential energy at displacement x is 1/2kx². Kinetic energy is whatever remains.

   KE = 1/2k(A² - x²)

2. Check the ends. At the mean position x = 0, KE takes its maximum value 1/2kA². At the extreme x = A the particle stops for an instant, so KE is zero. The graph must fall from a maximum to zero.
3. Check the shape. The slope is d(KE)/dx = -kx. It is zero at x = 0, so the curve starts flat, and it gets steeper as x approaches A. That is a downward-bending curve, not a straight line.
4. So. Only graph (c) starts flat at its maximum at x = 0 and curves down to zero at x = A. The answer is (c).

The idea to keep. For any energy-versus-x graph in SHM, write the formula first: PE = 1/2kx² opens upward, KE = 1/2k(A² - x²) opens downward, and total energy is a flat line.

Answer from the NTA final answer key. Solution by PrepWiser.