Which concepts are needed for the description of a periodic motion?

Match the following functions with their corresponding nature of motion, where $\omega$ is a constant:

List-$I$	List-$II$
$A$. $\sin^2 \omega t$	$I$. Periodic but not $SHM$ $(T = 2\pi/\omega)$
$B$. $\sin^3 \omega t$	$II$. Periodic but not $SHM$ $(T = \pi/\omega)$
$C$. $\sin \omega t + \cos \pi \omega t$	$III$. Non-periodic
$D$. $\cos \omega t + \cos 2\omega t$	$IV$. Periodic but not $SHM$ $(T = 2\pi/\omega)$

$A$ particle moves in the $x-y$ plane according to the equation $\overrightarrow{r} = (\widehat{i} + 2\widehat{j}) A \cos \omega t$. The motion of the particle is:

$A$ 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

If a $SHM$ is represented by $\frac{d^2x}{dt^2} + ax = 0$,its time period is:

Explain the concepts of a reference particle and a reference circle,and show that simple harmonic motion $(SHM)$ is the projection of uniform circular motion on a diameter of the reference circle.