No Restoring Force Proportional to Displacement: Simple harmonic motion requires a restoring force that is directly proportional to the displacement from a fixed equilibrium position and always

Here are two reasons why the motion of a ball passed repeatedly between two footballers is not simple harmonic motion:

1. No Restoring Force Proportional to Displacement: Simple harmonic motion requires a restoring force that is directly proportional to the displacement from a fixed equilibrium position and always directed towards that position ($F = -kx$). When a ball is passed, there is no such restoring force acting to pull it back to a central equilibrium point. Instead, the ball moves under the influence of an initial impulse, gravity, and air resistance.
2. No Fixed Equilibrium Position: For simple harmonic motion, the object must oscillate about a stable equilibrium position. In the case of passing a ball, the ball travels between two points (the players) and does not oscillate around a single, fixed central point. Its motion is a translation from one point to another, not an oscillation around an equilibrium.