Question 168: Oscillations

Question

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 $$x=$$ _________.

Accepted Answer

$$\begin{aligned}
& 	ext { Let total energy }=\mathrm{E}=\frac{1}{2} \mathrm{KA}^2 \
& \mathrm{U}=\frac{1}{2} \mathrm{~K}\left(\frac{\mathrm{A}}{3}ight)^2=\frac{\mathrm{KA}^2}{2 	imes 9}=\frac{\mathrm{E}}{9} \
& \mathrm{KE}=\mathrm{E}-\frac{\mathrm{E}}{9}=\frac{8 \mathrm{E}}{9} \
& 	ext { Ratio } \frac{	ext { Total }}{\mathrm{KE}}=\frac{\mathrm{E}}{\frac{8 \mathrm{E}}{9}}=\frac{9}{8} \
& \mathrm{x}=9
\end{aligned}$$

Oscillations

When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $\frac{x}{8}, where x=$ _________.

Integer / Numeric Answer Type