The maximum velocity of a body undergoing $S.H.M.$ is $0.2 \ m/s$ and its acceleration at $0.1 \ m$ from the mean position is $0.4 \ m/s^2$. The amplitude of the $S.H.M.$ is .... $m$

The velocity of a particle executing simple harmonic motion along the $x$-axis is described by the equation $v^2 = 50 - x^2$,where $x$ represents displacement. If the time period of the motion is $\frac{x}{7} \ \text{s}$,the value of $x$ is . . . . . . .

$A$ particle executes a linear $S.H.M.$ In two of its positions,the velocities are $V_1$ and $V_2$,and the accelerations are $a_1$ and $a_2$ respectively $(0 < a_1 < a_2)$. The distance between the positions is

The velocity of a particle executing a simple harmonic motion is $13 \ m/s$,when its distance from the equilibrium position $(Q)$ is $3 \ m$ and its velocity is $12 \ m/s$,when it is $5 \ m$ away from $Q$. The frequency of the simple harmonic motion is

What is the phase difference between the velocity and displacement of a particle executing $SHM$ (in $^{\circ}$)?

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?