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 ..... $Hz$.

For a particle showing motion under the force $F = -5(x - 2)$,the motion is ...........

The distance covered by a particle undergoing $SHM$ in one time period is (amplitude $= A$).

Write the equation that represents the relation between time period $(T)$ and angular frequency $(\omega)$.

For a particle performing linear $SHM$,its average speed over $1$ oscillation is ($A =$ amplitude of $SHM$,$n =$ frequency of oscillation). (in $A \ n$)

The figure shows the circular motion of a particle. The radius of the circle,the period,the sense of revolution,and the initial position are indicated in the figure. The simple harmonic motion of the $x$-projection of the radius vector of the rotating particle $P$ is