Question 173: Oscillations

Question

The amplitude of a particle executing SHM is $$3 \mathrm{~cm}$$. The displacement at which its kinetic energy will be $$25 \%$$ more than the potential energy is: __________ $$\mathrm{cm}$$

Accepted Answer

$A=3 \mathrm{~cm}$
$$
\begin{aligned}
& K=1.25 U \\
& \Rightarrow K+\frac{K}{1.25}=K_{\max } \\
& \Rightarrow \frac{9}{5} K=K_{\max } \\
& \Rightarrow  \frac{9}{5} \frac{1}{2} m v^{2}=\frac{1}{2} m v_{\max }^{2} \\
& \Rightarrow  \frac{9}{5}\left[\omega \sqrt{A^{2}-x^{2}}ight]^{2}=\omega^{2} A^{2} \\
& \Rightarrow 9\left(A^{2}-x^{2}ight)=5 A^{2} \\
& \Rightarrow  x^{2}=\frac{4 A^{2}}{9} \\
& \Rightarrow  x=\frac{2 A}{3} \\
& \Rightarrow  x=2 \mathrm{~cm}
\end{aligned}
$$

Oscillations

The amplitude of a particle executing SHM is $3 \mathrm{~cm}. The displacement at which its kinetic energy will be 25 \% more than the potential energy is: __________ \mathrm{cm}

Integer / Numeric Answer Type