Simple harmonic motion is the repetitive movement back and forth through an equillibrum or position, so that the maximum displacement on one side of this position is equall to the maximum displacement on the other side. The time interval of each complete vibration is the same and the force responsible for the motion is always directed toward the equillibrum position and is directly proportional to the distance from it.
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Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement.