The equation of $SHM$ of a particle is given as $2 \frac{d^2x}{dt^2} + 32x = 0$,where $x$ is the displacement from the mean position of rest. The period of its oscillation (in seconds) is

Explain periodic function.

Fill in the blanks:
$1.$ In $SHM$,......... quantities are always positive.
$2.$ $A$ periodic motion that obeys the force law ......... is only a simple harmonic motion.
$3.$ $A$ $SHO$ with a periodic time of $2 \ s$ starts its oscillation from the lower end of its path of motion; its phase will be .......... at time $t = 2 \ s$.

$A$ particle of mass $0.4 \text{ kg}$ executes simple harmonic motion of amplitude $0.4 \text{ m}$. When it passes through the mean position,its kinetic energy is $256 \times 10^{-3} \text{ J}$. If the initial phase of the oscillation is $\pi / 4$,then the equation of its motion is

The displacement of an oscillator is given by $x = a \sin \omega t + b \cos \omega t$,where $a, b$ and $\omega$ are constants. Then:

The graphs in the figure show that a quantity $y$ varies with displacement $d$ in a system undergoing simple harmonic motion. Which graph best represents the relationship obtained when $y$ is the time?