The equation of motion of a particle of mass $1\,g$ is $\frac{d^2x}{dt^2} + \pi^2x = 0$,where $x$ is displacement (in $m$) from the mean position. The frequency of oscillation is (in $Hz$):

Identify the function which represents a periodic motion.

If the displacement of a particle executing simple harmonic motion is given by $x = 0.5 \cos (125.6 t)$,then the time period of oscillation of the particle is nearly. (Here $x$ is displacement in metre and $t$ is time in second) (in $s$)

If the function $\sin^2 \omega t$ (where $t$ is time in seconds) represents a periodic motion,then the period of the motion is:

What is the projection of uniform circular motion?

$A$ particle is executing $SHM$ with an amplitude $A$. The distance travelled by the particle in one time period is