Answer
The motion of the shadow is not SHM.
Work Step by Step
Let $t=0$ when the plane is at the bottom of the circle and let $\theta = 0$ be the angle at the bottom of the circle. Let $R$ be the radius of the circle that the plane follows. Let $x$ be horizontal component of the plane's position around the circle. Let $x = 0$ be the center of the circle.
We can find an expression for $x$ in terms of time $t$:
$\frac{x}{R} = sin~\theta$
$x = R~sin~\theta$
If the angular speed was constant, we could describe the position $x$ with the equation $x = R~sin~(\omega~t)$. However, since the angular speed is not constant, we can not express $x$ in this form.
Therefore, the motion of the shadow is not SHM.
