If a simple harmonic oscillator has a displacement of $0.02\, m$ and an acceleration equal to $2.0\, m\, s^{-2}$ at any time,the angular frequency of the oscillator is equal to .... $rad\, s^{-1}$.

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 ..... $cm/s^2$.

For a particle performing $S.H.M.$, the displacement-time graph is shown. For that particle, the force-time graph is correctly represented by which of the following?

For a particle executing simple harmonic motion, the displacement-time $(x-t)$ graph is as shown in the figure. The acceleration of the particle at $t=\frac{4}{3} \,s$ is

Obtain instantaneous acceleration of a $SHM$ particle with the help of reference circle.

$A$ book is resting on a shelf that is undergoing vertical simple harmonic oscillations with an amplitude of $2.5 \,cm$. What is the minimum frequency of oscillation of the shelf for which the book will lose contact with the shelf (in $,Hz$)? (Assume that $g = 10 \,m/s^2$)