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 =

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Solution

Q.
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 = __________. [2024]

Ans.
(9) $E = \frac{1}{2} K A^{2}$

$U = \frac{1}{2} K {(\frac{A}{3})}^{2} = \frac{K A^{2}}{2 \times 9} = \frac{E}{9}$

$K E = E - \frac{E}{9} = \frac{8 E}{9}$

Ratio = $\frac{E}{K E} = \frac{E}{\frac{8 E}{9}} = \frac{9}{8} \Rightarrow x = 9$

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