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To and from motion of an object about its mean position
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Oscillatory motion is defined as the to and fro motion of an object from its mean position. ... To describe mechanical oscillation, the term vibration is used which is found in a swinging pendulum.
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Thus, the particle continues to move towards the other side of the equilibrium position and then again a force develops tending to pull it back. This was, in absence of damping forces, the particle continues it's to and fro motion about the equilibrium potion. This is what constitutes a simple harmonic motion.
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