$A$ 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 .........

If the displacement of a particle executing $SHM$ is given by $y = 0.30 \sin(220t + 0.64)$ in meters,then the frequency and maximum velocity of the particle are:

$A$ $S.H.M.$ is represented by $x = 5\sqrt{2} (\sin 2\pi t + \cos 2\pi t).$ The amplitude of the $S.H.M.$ is .... $cm$.

Which of the following functions of time represent $(a)$ periodic and $(b)$ non-periodic motion? Give the period for each case of periodic motion $[\omega$ is any positive constant].
$(i)$ $\sin \omega t + \cos \omega t$
$(ii)$ $\sin \omega t + \cos 2\omega t + \sin 4\omega t$
$(iii)$ $e^{-\omega t}$
$(iv)$ $\log(\omega t)$

Write the phase difference between displacement and velocity,displacement and acceleration,and velocity and acceleration for a particle executing Simple Harmonic Motion $(SHM)$.

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