Which graph represents the difference between total energy and potential energy of a particle executing SHM vs it's distance from mean position ?

Solution

Physics sir · 3 steps

Total energy minus potential energy is just kinetic energy, so sketch K against x.

1. Name the difference. In SHM the total energy E = 1/2kA² stays constant, and U = 1/2kx². Their difference is the kinetic energy.

   E - U = 1/2kA² - 1/2kx² = 1/2k(A² - x²)

2. Read the shape. This depends on x², so the graph is the same at x and -x. It is largest, 1/2kA², at x = 0 and falls to zero at x = ± A. It is a smooth curve opening downward with a rounded top, not straight lines.
3. So. The graph must be a smooth, symmetric hump with its peak at the mean position and zero at both extremes. That is graph (a).

The idea to keep. In SHM, E - U is always the kinetic energy 1/2k(A² - x²). Kinetic energy is greatest at the mean position, zero at the extremes, and depends only on x², so its graph is symmetric.

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