The acceleration $a$ of a particle undergoing $S.H.M.$ is shown in the figure. Which of the labelled points corresponds to the particle being at $-x_{max}$?

$A$ 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 $g = 10 \,m/s^2$)

Obtain the force law for $SHM$ from the displacement of $SHM$ particle.

$A$ horizontal platform with a small object placed on it executes a linear $S.H.M.$ in the vertical direction. The amplitude of oscillation is $40 \text{ cm}$. What should be the least period of these oscillations, so that the object is not detached from the platform (in $\pi \text{ s}$)? [Take $g = 10 \text{ m/s}^2$]

$A$ body oscillates with $S.H.M.$ according to the equation $x = (5.0 \, m) \cos [(2 \pi \, rad \, s^{-1}) t + \pi / 4]$. At $t = 1.5 \, s$,its acceleration is ....... $m / s^2$.

What is the phase difference between the displacement and acceleration of a particle executing $SHM$?