$A$ simple pendulum starts oscillating simple harmonically from its mean position $(x=0)$ with amplitude '$a$' and periodic time '$T$'. The magnitude of velocity of the pendulum at $x=\frac{a}{2}$ is

If a particle under $S.H.M.$ has a time period of $0.1 \ s$ and an amplitude of $2 \times 10^{-3} \ m$,what is its maximum velocity?

$A$ particle executes $SHM$. Its velocities are $v_1$ and $v_2$ at displacements $x_1$ and $x_2$ from the mean position,respectively. The frequency of oscillation will be

$A$ particle executes simple harmonic motion with a periodic time of $0.05 \, s$ and an amplitude of $4 \, cm$. What is its maximum velocity?

$A$ particle executing simple harmonic motion has a maximum acceleration of $24 \ m/s^2$ and a maximum velocity of $16 \ m/s$. What is its amplitude?

$A$ particle is executing simple harmonic motion with amplitude $A$. At a distance $x$ from the mean position,when the particle is moving towards the extreme position,it receives a blow in the direction of motion which instantaneously doubles its velocity. What is the new amplitude of the particle? (Frequency remains constant during the motion)