The graph between velocity and displacement of a particle executing $S.H.M.$ is

The equation of motion of a particle performing linear $S.H.M$ is $x=5 \sin \left[4 t-\frac{\pi}{6}\right]$,where $x$ is its displacement in $cm$. The velocity of the particle when its displacement is $3 \ cm$ is: (in $cm/s$)

$A$ spring executes $SHM$ with a mass of $10\,kg$ attached to it. The force constant of the spring is $10\,N/m$. If at any instant its velocity is $40\,cm/s$,the displacement will be .... $m$ (where amplitude is $0.5\,m$).

The angular velocities of three bodies in simple harmonic motion are ${\omega _1}, {\omega _2}, {\omega _3}$ with their respective amplitudes as ${A_1}, {A_2}, {A_3}$. If all the three bodies have the same maximum velocity,then:

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 performing simple harmonic motion about $x = 0$ with an amplitude $a$ and periodic time $T$. The speed of the particle at $x = \frac{a}{3}$ will be