Question

An object of mass $0.2\, kg$ executes SHM along $x$-axis with a frequency of $\frac{16}{\pi} Hz$. At the position, $x =0.04 \,m$ the object has kinetic energy $0.5 \,J$ and potential energy $0.4\, J$. The amplitude of oscillation is ______m

Answer 1

$TE =0.5+0.4=0.9\, J$
$TE =\frac{1}{2} m \omega^{2} a ^{2} $
$\Rightarrow TE =\frac{1}{2} m 4 \pi^{2} v^{2} a ^{2} $
$\Rightarrow 0.9 =\frac{1}{2} \times 0.2 \times 4 \pi^{2}\left(\frac{16}{\pi}\right)\left(\frac{16}{\pi}\right) a ^{2}$
$\Rightarrow a =\sqrt{\frac{9}{4 \times 16 \times 16}} $
$=\frac{3}{32} $
$\therefore a \approx 0.09\, m$