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A mass $0.4 \mathrm{~kg}$ performs S.H.M. with a frequency $\frac{16}{\pi} \mathrm{Hz}$. At a certain displacement it has kinetic energy $2 \mathrm{~J}$ and potential energy $1.2 \mathrm{~J}$. The amplitude of oscillation is
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The correct answer is:
0.125 m
$$
\begin{aligned}
& \mathrm{m}=0.4 \mathrm{~kg}, \mathrm{f}=\frac{16}{\pi} \mathrm{Hz}, \mathrm{K} \cdot \mathrm{E} \cdot=2 \mathrm{~J}, \text { P.E. }=1.2 \mathrm{~J} \\
& \omega=2 \pi \mathrm{f}=2 \pi \times \frac{16}{\pi}=32 \mathrm{rad} / \mathrm{s}
\end{aligned}
$$
Total energy T.E. $=2+1.2=3.2 \mathrm{~J}$
$$
\begin{aligned}
& \mathrm{TE}=\frac{1}{2} \mathrm{~m}^2 \mathrm{~A}^2 \\
& \therefore \mathrm{A}^2=\frac{2(\mathrm{TE})}{\mathrm{m} \omega^2}=\frac{2 \times 3.2}{0.4 \times(32)^2}=\frac{6.4}{0.4 \times(32)^2}=\frac{16}{(32)^2} \\
& \therefore \mathrm{A}=\frac{4}{32}=\frac{1}{8}=0.125 \mathrm{~m}
\end{aligned}
$$
\begin{aligned}
& \mathrm{m}=0.4 \mathrm{~kg}, \mathrm{f}=\frac{16}{\pi} \mathrm{Hz}, \mathrm{K} \cdot \mathrm{E} \cdot=2 \mathrm{~J}, \text { P.E. }=1.2 \mathrm{~J} \\
& \omega=2 \pi \mathrm{f}=2 \pi \times \frac{16}{\pi}=32 \mathrm{rad} / \mathrm{s}
\end{aligned}
$$
Total energy T.E. $=2+1.2=3.2 \mathrm{~J}$
$$
\begin{aligned}
& \mathrm{TE}=\frac{1}{2} \mathrm{~m}^2 \mathrm{~A}^2 \\
& \therefore \mathrm{A}^2=\frac{2(\mathrm{TE})}{\mathrm{m} \omega^2}=\frac{2 \times 3.2}{0.4 \times(32)^2}=\frac{6.4}{0.4 \times(32)^2}=\frac{16}{(32)^2} \\
& \therefore \mathrm{A}=\frac{4}{32}=\frac{1}{8}=0.125 \mathrm{~m}
\end{aligned}
$$
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