Answer
No, the motion is not simple harmonic.
Work Step by Step
Clearly the given motion is periodic. For a motion to be simple harmonic the restoring force should be proportional to the displacement from the mean position.
$$F \propto x$$
But the force acting here is the weight of ball.
$$F = mg $$
which is constant and not proportional to the displacement from mean position.
Hence, the given motion is not simple harmonic.
