$SHM$ is associated with what kind of motion?

Show that the motion of a particle represented by $y = \sin \omega t - \cos \omega t$ is simple harmonic with a period of $\frac{2\pi}{\omega}$.

Which of the following relationships between the acceleration $a$ and the displacement $x$ of a particle involve simple harmonic motion?
$(a)\; a=0.7 x$
$(b)\; a=-200 x^{2}$
$(c)\; a=-10 x$
$(d)\; a=100 x^{3}$

$A$ particle is moving with constant angular velocity along the circumference of a circle. Which of the following statements is true?

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

What is constant in $S.H.M.$?