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 = _________.

Step-by-step solution

The total energy of the harmonic oscillator is given by the formula E = 1 2 k A 2 . . . 1 where, k is the force constant and A is the amplitude. The potential energy of the oscillator at the given displacement can be written as U = 1 2 k A 3 2 = k A 2 2 × 9 = E 9 Hence, its kinetic energy is given by K E = E - E 9 = 8 E 9 Thus, the required ratio is E K E = E 8 E 9 = 9 8 Hence, x = 9 .