For a simple harmonic motion represented by the equation $y = 0.30 \sin (220 \, t + 0.64) \ m$,what are the frequency and maximum velocity,respectively?

The displacement of a particle is given by the relation $x = 4(\cos \pi t + \sin \pi t)$. The amplitude of the particle is

The figure shows the circular motion of a particle. The radius of the circle is $B$. The particle starts at $t=0$ from the positive $y$-axis and moves clockwise. The simple harmonic motion of the $x$-projection of the radius vector of the rotating particle is given by:

$A$ particle free to move along the $x$-axis has potential energy given by $U(x) = k[1 - \exp(-x^2)]$ for $-\infty \le x \le +\infty$,where $k$ is a positive constant of appropriate dimensions. Then:

The displacement of a particle performing linear $S.H.M.$ is given by $y = A \cos[\pi(t + \phi)]$. If at $t = 0$, the displacement is $y = 2 \text{ cm}$ and velocity is $2\pi \text{ cm/s}$, the value of amplitude $A$ in $\text{cm}$ is

Show that simple harmonic motion may be regarded as the projection of uniform circular motion along a diameter of the circle.