JEE MAIN - Physics (2024 - 29th January Morning Shift - No. 28)
When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $$\frac{x}{8}$$, where $$x=$$ _________.
Answer
9
Explanation
$$\begin{aligned}
& \text { Let total energy }=\mathrm{E}=\frac{1}{2} \mathrm{KA}^2 \\
& \mathrm{U}=\frac{1}{2} \mathrm{~K}\left(\frac{\mathrm{A}}{3}\right)^2=\frac{\mathrm{KA}^2}{2 \times 9}=\frac{\mathrm{E}}{9} \\
& \mathrm{KE}=\mathrm{E}-\frac{\mathrm{E}}{9}=\frac{8 \mathrm{E}}{9} \\
& \text { Ratio } \frac{\text { Total }}{\mathrm{KE}}=\frac{\mathrm{E}}{\frac{8 \mathrm{E}}{9}}=\frac{9}{8} \\
& \mathrm{x}=9
\end{aligned}$$
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