Average velocity of a particle executing $SHM$ in one complete vibration is

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

Can an oscillatory motion be non-periodic?

$A$ particle is executing $SHM$ about $y=0$ along the $y$-axis. Its position at an instant is given by $y = (7 \, m) \sin(\pi t)$. Its average velocity for the time interval $0$ to $0.5 \, s$ is ........... $m/s$.

The motion of a particle varies with time according to the relation $y = a(\sin \omega \,t + \cos \omega \,t)$,then

$A$ point particle of mass $0.1 \ kg$ is executing $S.H.M.$ with an amplitude of $0.1 \ m$. When the particle passes through the mean position,its kinetic energy is $8 \times 10^{-3} \ J$. Obtain the equation of motion of this particle if the initial phase of oscillation is $45^{\circ}$.