When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is x/8, where x= _________.

Solution

Physics sir · 3 steps

Write both energies in terms of amplitude: total energy depends on A², kinetic energy on A² - y².

1. Two energies. In SHM the total energy is constant, E = 1/2kA². At displacement y the kinetic energy is K = 1/2k(A² - y²).

   E/K = A²/(A² - y²)

2. Put in numbers. With y = A/3, y² = A²/9. So A² - y² = 8A²/9, and the ratio is A²/(8A²/9) = 9/8.
3. So. x/8 = 9/8, which gives x = 9.

The common slip: 12. Using y = A/3 without squaring it makes the kinetic energy 2/3 of the total, so the ratio comes out as 3/2 = 12/8 and gives 12, not 9.

The idea to keep. Energy in SHM goes as displacement squared. Potential energy is 1/2ky², kinetic energy is 1/2k(A² - y²), and the two always add up to 1/2kA².

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