In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.

Solution

Physics sir · 3 steps

Halfway in distance is not halfway in energy: PE grows as x², so at A/2 it is only a quarter.

1. Energy formulas. Total energy stays fixed at E = 1/2kA². Potential energy at displacement x is U = 1/2kx², and kinetic energy is whatever is left: K = 1/2k(A² - x²).
2. Midway point. Midway between the mean position and the extreme means x = A/2, so x² = A²/4.

   K/E = (A² - x²)/A² = 1 - 1/4 = 3/4

3. So. Potential energy is 1/4 of the total and kinetic energy is 3/4, which is option (b).

The idea to keep. In SHM, U/E = x²/A² and K/E = 1 - x²/A². Square the fraction of amplitude before you split the energy.

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