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?

In case of a simple harmonic motion,if the velocity is plotted along the $X$-axis and the displacement (from the equilibrium position) is plotted along the $Y$-axis,the resultant curve is an ellipse with the ratio:
Major axis (along $X$) $= 20 \pi \times$ Minor axis (along $Y$).
What is the frequency of the simple harmonic motion?

$A$ particle is executing simple harmonic motion. If the force acting on the particle at a position is $86.6 \%$ of the maximum force on it,then the ratio of its velocity at that point and its maximum velocity is

For a simple harmonic motion given by the equation $x = 5 \sin (4t - \frac{\pi}{6}) \, m$,what is the velocity when its displacement is $3 \, m$ (in $, m/s$)?

The displacement of a particle executing $SHM$ is given by $x = 10 \sin \left(\omega t + \frac{\pi}{3}\right) \ m$. The time period of motion is $3.14 \ s$. The velocity of the particle at $t = 0$ is . . . . . . $m/s$.

$A$ particle executes simple harmonic motion with a time period $0.6 \,s$ and amplitude $10 \,cm$. Find the mean velocity of the particle over the time interval during which it travels a distance $5 \,cm$ starting from the equilibrium position.