The maximum speed of a particle executing $S.H.M.$ is $1 \ m/s$ and its maximum acceleration is $1.57 \ m/s^2$. The time period of the particle will be .... $s$.

$A$ particle is performing $S.H.M.$ with an amplitude $4 \,cm$. At the mean position, the velocity of the particle is $12 \,cm/s$. When the speed of the particle becomes $6 \,cm/s$, the distance of the particle from the mean position is:

$A$ particle executes $S.H.M.$ starting from the mean position. Its amplitude is '$a$' and its periodic time is '$T$'. At a certain instant,its speed '$u$' is half that of maximum speed $V_{\text{max}}$. The displacement of the particle at that instant is

$A$ particle performs simple harmonic motion with amplitude $A$. Its speed is trebled at the instant that it is at a distance $\frac{2A}{3}$ from the equilibrium position. The new amplitude of the motion is

Maximum velocity and maximum acceleration of a particle executing $SHM$ are $\beta$ and $\alpha$ respectively. What will be its frequency?

For a simple harmonic motion with amplitude $A$ and time period $T$,what is the velocity at $x = \frac{A}{2}$?