This is the position-time graph of a mass on a spring. What can you say about the velocity and force at the instant indicated by the dashed line? (Positive direction is to the right.)

$A$ particle moving along the $X$-axis executes simple harmonic motion. The force acting on it is given by: (Where $A$ and $K$ are positive constants)

$A$ 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 $A$.

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

The displacement of a particle performing $S.H.M.$ is given by $x=5 \sin (3 t+3)$,where $x$ is in $cm$ and $t$ is in $s$. The maximum acceleration of the particle will be (in $cm \ s^{-2}$)

The displacement of a particle varies with time as $x = 12 \sin \omega t - 16 \sin^3 \omega t$ (in $cm$). If its motion is $S.H.M.$,then its maximum acceleration is