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 vibrating simple harmonically has an acceleration of $16 \ cm/s^2$ when it is at a distance of $4 \ cm$ from the mean position. Its time period is: (in $s$)

Acceleration of a particle,executing $SHM$,at its mean position is

The variation of displacement with time of a simple harmonic motion $(SHM)$ for a particle of mass $m$ is represented by $y = 2 \sin \left(\frac{\pi t}{2} + \phi\right) \text{ cm}$. The maximum acceleration of the particle is

$A$ piston is performing $S.H.M.$ in the vertical direction with a frequency of $0.5 \,Hz$. $A$ block of $10 \,kg$ is placed on the piston. The maximum amplitude of the system such that the block remains in contact with the piston is: (in $\,m$)

$A$ particle is in linear simple harmonic motion between two points,$A$ and $B$,$10 \; cm$ apart. Take the direction from $A$ to $B$ as the positive direction and give the signs of velocity,acceleration,and force on the particle when it is:
$(a)$ at the end $A$.
$(b)$ at the end $B$.
$(c)$ at the mid-point of $AB$ going towards $A$.
$(d)$ at $2 \; cm$ away from $B$ going towards $A$.
$(e)$ at $3 \; cm$ away from $A$ going towards $B$.
$(f)$ at $4 \; cm$ away from $B$ going towards $A$.