Simple harmonic motion is basically the repeated back and forth movement through a central position, such that the maximum displacement on one side of that position is equal to the maximum displacement on the other side. Each complete vibration’s time interval is the same. The force responsible for the motion is always directed towards the direction of equilibrium and is directly proportional to the distance from it.
Some common examples of SHM are pendulums. If the resting position of the pendulum is assumed to be the center, then when the pendulum moves, it is observed that the distance it covers on either side of the center is equal, and the pendulum always moves toward the center after covering it’s maximum distance. We shall refer to the center as equilibrium.
Springs usually have SHM. Springs have their own natural “spring constants” which define how stiff they are. Hooke’s law is a famous law that explains the SHM and gives a formula for the force applied using the spring constant.
When applied to a spring, we can observe that when the spring is stretched in both directions then both the ends of the spring recoil toward equilibrium. This is very similar to how a pendulum behaves even though it does not move in a circular fashion.
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