Terms
Firstly, let's define two terms that are necessary to understand simple harmonic motion:
Equilibrium Position: This is where the vibrating object resides when not disturbed. In other words, the object that is swinging or oscillating will do so about this position.
Restoring force: When an object is displaced from its equilibrium, the restoring force is a force acting on the object from an outside factor (usually will be the force of gravity), whose vector will always point opposite of the objects displacement. This force tries to restore the object towards equilibrium
During simple harmonic motion the restoring force will always be proportional to the displacement from equilibrium. If you're given a graph and asked if it's simple harmonic motion, it should always be sinusoidal, where the midpoint is the equilibrium point.
Equilibrium Position: This is where the vibrating object resides when not disturbed. In other words, the object that is swinging or oscillating will do so about this position.
Restoring force: When an object is displaced from its equilibrium, the restoring force is a force acting on the object from an outside factor (usually will be the force of gravity), whose vector will always point opposite of the objects displacement. This force tries to restore the object towards equilibrium
During simple harmonic motion the restoring force will always be proportional to the displacement from equilibrium. If you're given a graph and asked if it's simple harmonic motion, it should always be sinusoidal, where the midpoint is the equilibrium point.