The displacement $x$ (in metres) of a particle performing simple harmonic motion is related to time $t$ (in seconds) as $x = 0.05 \cos \left( 4 \pi t + \frac{\pi}{4} \right)$. The frequency of the motion will be ..... $Hz$.

Obtain the expression of displacement from the force law for simple harmonic motion.

$A$ particle is executing simple harmonic motion with an amplitude $A$ and time period $T$. The displacement of the particle after $2T$ time from its initial position is

$A$ particle executes simple harmonic motion according to the equation $4 \frac{d^2 x}{d t^2} + 320 x = 0$. Its time period of oscillation is .........

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 $t = 2 \ s$.

Draw plots for initial phase $\phi = 0$ for different periods.