$A$ simple pendulum performs simple harmonic motion about $x=0$ with an amplitude $a$ and time period $T$. The speed of the pendulum at $x=a/2$ will be

$A$ particle executes linear $S.H.M.$ with amplitude $A = 4 \text{ cm}$. The magnitude of velocity and acceleration is equal when it is at a distance $x = 3 \text{ cm}$ from the mean position. The time period of the oscillation is:

An object undergoing simple harmonic motion takes $0.5 \text{ s}$ to travel from one point of zero velocity to the next such point. The angular frequency of the motion is,

The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of $1.0 \; m$. If the piston moves with simple harmonic motion with an angular frequency of $200 \; rad/min$,what is its maximum speed in $m/min$?

$A$ particle executing $SHM$ along a straight line has zero velocity at points $A$ and $B$ whose distances from $O$ on the same line $OAB$ are $a$ and $b$,respectively. If the velocity at the midpoint between $A$ and $B$ is $v$,then its time period is

$A$ simple pendulum performs simple harmonic motion about $X = 0$ with an amplitude $A$ and time period $T$. The speed of the pendulum at $X = \frac{A}{2}$ will be