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?

$A$ particle of mass $5 \,g$ is executing $S.H.M.$ with an amplitude $0.3 \,m$ and period $\frac{\pi}{5} \,s$. The maximum value of the force acting on the particle is (in $\,N$)

The displacement of a particle moving in $S.H.M.$ at any instant is given by $y = a \sin \omega t$. The acceleration after time $t = \frac{T}{4}$ is (where $T$ is the time period).

What is the force constant of a particle executing $SHM$?

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

The graphs in the figure show that a quantity $y$ varies with displacement $d$ in a system undergoing simple harmonic motion. Which graph best represents the relationship obtained when $y$ is the unbalanced force acting on the system?