Question 314: Oscillations

Question

For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at certain displacement '$$x$$' from the mean position. If '$$A$$' is the amplitude of S.H.M the value of '$$x$$' is

Accepted Answer

Potential energy: $$U=\frac{1}{2} m \omega^2 x^2$$ and
Kinetic energy: $$K=\frac{1}{2} m \omega^2\left(A^2-x^2ight)$$
Given: Potential energy $$=8 	imes$$ Kinetic energy
$$\begin{aligned}
& 	herefore \quad \mathrm{U}=8 \mathrm{~K} \
& \frac{1}{2} m \omega^2 x^2=8 	imes \frac{1}{2} m \omega^2\left(A^2-x^2ight) \
& x^2=8 A^2-8 x^2 \
& 9 x^2=8 A^2 \
& x^2=\frac{8 A^2}{9} \
& x=\frac{2 \sqrt{2} A}{3} \
\end{aligned}$$

Answer

$$\frac{\mathrm{A} \sqrt{2}}{3}$$

Answer

$$\mathrm{A} \sqrt{3}$$

Answer

$$\frac{2 \sqrt{2} \mathrm{~A}}{3}$$

Answer

$$\frac{\mathrm{A}}{\sqrt{2}}$$

Oscillations

For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at certain displacement '$x' from the mean position. If 'A' is the amplitude of S.H.M the value of 'x$' is

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