$A$ particle executing simple harmonic motion of amplitude $5\, cm$ has a maximum speed of $31.4\, cm/s$. The frequency of its oscillation is ..... $Hz$.

The function $\sin^2(\omega t)$ represents:

$A$ stone is swinging in a horizontal circle $0.8 \, m$ in diameter at $30 \, rev/min$. $A$ distant horizontal light beam causes a shadow of the stone to be formed on a nearly vertical wall. The amplitude and period of the simple harmonic motion for the shadow of the stone are:

The motion of a particle is described by the equation $a = -bx$,where $a$ is the acceleration,$x$ is the displacement from the equilibrium position,and $b$ is a constant. The periodic time will be

Why is the periodic time $T = \frac{2\pi}{\omega}$ taken for the function $f(t) = A \cos \omega t$?

$A$ particle is oscillating according to the equation $X = 7 \cos(0.5 \pi t)$,where $t$ is in seconds. The particle moves from the position of equilibrium to maximum displacement in time ..... $s$.