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

The oscillation of a body on a smooth horizontal surface is represented by the equation $x = A \cos \omega t$,where $x$ is the displacement at time $t$ and $\omega$ is the angular frequency of oscillation. Which one of the following graphs correctly shows the variation of acceleration $a$ with time $t$?

Two simple harmonic motions of angular frequency $100 \, rad \, s^{-1}$ and $1000 \, rad \, s^{-1}$ have the same displacement amplitude. The ratio of their maximum acceleration is

The maximum acceleration of a particle in $SHM$ is made two times keeping the maximum speed constant. This is possible when:

$A$ particle of mass $0.3 \, kg$ is subjected to a force $F = -kx$ with $k = 15 \, N/m$. What will be its initial acceleration if it is released from a point $20 \, cm$ away from the origin? (in $m/s^2$)