The kinetic energy, $K$ of a body performing simple harmonic motion varies with time $t$, is indicated in…
The kinetic energy, $K$ of a body performing simple harmonic motion varies with time $t$, is indicated in graph
Solution
Kine tic energy of a body performing simple harmonic motion is given as
$
K=\frac{1}{2} m v^2
$
where,
$
\begin{aligned}
& v=\frac{d y}{d t}=\frac{d}{d t} \cdot a \sin \omega t \quad[\because y=a \sin \omega t] \\
& v=a \omega \cos \omega t
\end{aligned}
$
$\therefore$ From Eq. (i), we get
$
\begin{aligned}
& K=\frac{1}{2} m(a \omega \cos \omega t)^2=\frac{1}{2} m a^2 \omega^2 \cos ^2 \omega t \\
& K=\frac{1}{2} m a^2 \omega^2\left(\frac{1+\cos 2 \omega t}{2}\right) \quad \ldots(\text { i })
\end{aligned}
$
The graph represented in option (1) is correct for expression of kinetic energy represented by Eq. (i)
