Q 11-13-059JEE MainJEE Main 2024 (29 Jan, Shift 1)Easy
When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $\dfrac{x}{8}$, where $x =$ ______.
Numerical value type. Enter your answer.
Answer: 9
$$E = \frac12kA^2,\qquad K = \frac12k\left(A^2 - \frac{A^2}{9}\right) = \frac89E$$
$$\frac EK = \frac98 \;\Rightarrow\; x = 9$$
Solution by Sreeraj P, M.Sc Physics