If the acceleration of the vibrating body directly varies with the displacement of the body from the mean position and always directed to the mean position, the motion of that body is called simple harmonic motion.
- simple pendulum
- mass spring system
- a steel ruler clamped to a bench oscillates when its free end is displaced sideways.
- a steel ball rolling in a curved dish
- a swing
Thus to get S.H.M a body is displaced away from its rest position and then released. The body oscillates due to restoring force. Under the action of this restoring force the body accelerates and overshoots the rest position due to inertia. The restoring force than pulls it back.
The restoring force is always directed towards the mean position and so the acceleration is also directed towards the mean or rest position.
Hope you are doing well. As per your query simple harmonic motion is a repetitive movement (https://www.britannica.com/science/motion-mechanics) back and forth through an equilibrium (https://www.merriam-webster.com/dictionary/equilibrium) , or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side. The time interval of each complete vibration is the same. The force (https://www.britannica.com/science/force-physics) responsible for the motion is always directed toward the equilibrium position and is directly proportional to the distance from it. The examples for the same are - the motion of a pendulum, the motion of vibrating mass attached to spring.
In the simple harmonic motion, the displacement of the object is always in the opposite direction of the restoring force.
And, the simple harmonic motion is always oscillatory.
Simple harmonic motion examples: the motion of a pendulum, motion of a spring, etc.
Hope it helps!