$A$ particle of mass $5 \ g$ performs simple harmonic motion with an amplitude of $10 \ cm$. Its maximum velocity is $100 \ cm/s$. At what distance from the mean position will its velocity be $50 \ cm/s$?

$A$ 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 performs linear $S.H.M.$ When the displacement of the particle from the mean position is $3 \ cm$ and $4 \ cm$,the corresponding velocities are $8 \ cm/s$ and $6 \ cm/s$ respectively. Its periodic time 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

$A$ body is performing simple harmonic motion with amplitude $A$ and time period $T$. The variation of its acceleration $(f)$ with time $(t)$ is shown in the figure. If at time $t$,the velocity of the body is $v$,which of the following graphs correctly represents the variation of velocity $(v)$ with time $(t)$?

$A$ particle of mass $m$ is performing linear simple harmonic motion. Its equilibrium position is at $x = 0$,the force constant is $K$,and the amplitude of $SHM$ is $A$. The maximum power supplied by the restoring force to the particle during $SHM$ will be: