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A particle of mass $4 \mathrm{~kg}$ is executing SHM. Its displacement is given by the equation $y=8 \cos [100 t+\pi / 4] \quad \mathrm{cm}$. Its maximum kinetic energy is
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The correct answer is:
$128 \mathrm{~J}$
Equation of particle executing SHM
$$
y=8 \cos \left[100 t+\frac{\pi}{4}\right] \mathrm{cm}
$$
Here, $\quad \omega=100 \mathrm{rad} / \mathrm{s}, a=8 \mathrm{~cm}$
$$
\begin{aligned}
& \text { Maximum kinetic energy }=\frac{1}{2} m \omega^2 a^2 \\
& =\frac{1}{2} \times 4 \times 100 \times 100 \times\left(8 \times 10^{-2}\right)^2 \\
& =128 \mathrm{~J} \\
&
\end{aligned}
$$
$$
y=8 \cos \left[100 t+\frac{\pi}{4}\right] \mathrm{cm}
$$
Here, $\quad \omega=100 \mathrm{rad} / \mathrm{s}, a=8 \mathrm{~cm}$
$$
\begin{aligned}
& \text { Maximum kinetic energy }=\frac{1}{2} m \omega^2 a^2 \\
& =\frac{1}{2} \times 4 \times 100 \times 100 \times\left(8 \times 10^{-2}\right)^2 \\
& =128 \mathrm{~J} \\
&
\end{aligned}
$$
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