Question

What fraction of the total energy of a SHO is kinetic when the displacement is one third the amplitude

Answer 1

Answer:

The fraction of kinetic energy to the total energy is $\frac{K}{T}=\frac{8}{9}$.

Explanation:

displacement is one third of the amplitude.

Let the amplitude is A.

x= A/3

The kinetic energy of the body executing SHM is

$K = 0.5 mw^2(A^2 - x^2)\\\\K = 0.5 m w^2 \left ( A^2 -\frac{A^2}{9} \right )\\\\K = 0.5 mw^2\times \frac{8A^2}{9}......(1)$

The total energy is

$T =0.5 mw^2A^2 ..... (2)$

Divide (1) by (2)

$\frac{K}{T}=\frac{8}{9}$