$A$ $0.10\, kg$ block oscillates back and forth along a horizontal surface. Its displacement from the origin is given by: $x = (10\,cm)\cos [(10\,rad/s)\,t + \pi /2\,rad]$. What is the maximum acceleration experienced by the block?

$A$ particle performing $S$.$H$.$M$. when displacement is '$x$',the potential energy and restoring force acting on it are denoted by '$E$' and '$F$' respectively. The relation between $x, E$ and $F$ is

$A$ 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 $A$.

$A$ 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 executes harmonic motion with an angular velocity and maximum acceleration of $3.5\, rad/s$ and $7.5\, m/s^2$ respectively. The amplitude of oscillation is .... $m$

The weight suspended from a spring oscillates up and down. The acceleration of the weight will be zero at