Can an oscillatory motion be non-periodic?

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

The displacement of a particle in an oscillatory motion at a time $t$ is given by $x = 8 \sin \frac{\pi t}{4} \text{ cm}$. Calculate its displacement in the time interval $t = 0 \text{ s}$ to $t = 2 \text{ s}$. (in $\text{ cm}$)

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

$A$ particle executing $SHM$ of amplitude $a$ has a displacement of $-\frac{a}{2}$ at $t = \frac{T}{4}$ and a positive velocity. Find the initial phase of the particle.

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