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  4. The displacement of a particle varies with time as x=12 sin ω t-16 sin 3 ω t( in cm ). If its motion is S.H.M., then its maximum acceleration is

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Q. The displacement of a particle varies with time as $x=12$ $\sin \,\omega t-16 \sin ^{3} \,\omega t($ in $cm )$. If its motion is S.H.M., then its maximum acceleration is

Oscillations

Solution:

$x=12 \sin \omega t-16 \sin ^{3} \omega t=4\left[3 \sin \omega t-4 \sin ^{3} \omega t\right]$
$=4[\sin 3 \omega t]\left( By\right.$ using $\left.\sin 3 \theta=3 \sin \theta-4 \sin ^{3} \theta\right)$
$\therefore $ maximum acceleration $A_{\max }=(3 \omega)^{2} \times 4=36 \omega^{2}$