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 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 $t$?

$A$ particle is performing $S.H.M.$ starting from the extreme position. The graphical representation shows that between displacement and acceleration,there is a phase difference of:

The displacement of an oscillating particle varies with time $t$ (in seconds) according to the equation $y (cm) = \sin \left[ \frac{\pi}{2} \left( \frac{t}{2} + \frac{1}{3} \right) \right]$. The maximum acceleration of the particle is approximately ..... $cm/s^2$.

The amplitude of a particle executing $S.H.M.$ with a frequency of $60 \, Hz$ is $0.01 \, m$. The maximum value of the acceleration of the particle is

For a particle executing $SHM$, determine the ratio of the average acceleration of the particle between the extreme position and the equilibrium position with respect to the maximum acceleration.