The amplitude and the time period in a $S.H.M.$ are $0.5\, cm$ and $0.4\, s$ respectively. If the initial phase is $\pi/2$ radian,then the equation of $S.H.M.$ will be:

Which one of the following equations of motion represents simple harmonic motion? (Where $k, k_0, k_1$ and $a$ are all positive constants)

$A$ particle moves with simple harmonic motion in a straight line. In the first $\tau \, s,$ after starting from rest,it travels a distance $a,$ and in the next $\tau \, s,$ it travels $2a$ in the same direction. Then:

The function of time representing a simple harmonic motion with a period of $\frac{\pi}{\omega}$ is :

$A$ 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 executing $S.H.M.$ is given by $x = 0.01 \sin 100\pi (t + 0.05)$,where $x$ is in metres and $t$ is in seconds. The time period is ..... $sec$.