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The particle undergoing simple harmonic motion is called as simple harmonic oscillator. The displacement of the particle is given by,
The linear velocity of a particle undergoing simple harmonic motion is given as:
The acceleration of a particle undergoing simple harmonic motion is given by,
Thus, we can write the relationship between the acceleration and displacement as:
For a particle undergoing simple harmonic motion the corresponding figures for its displacement, velocity and acceleration are as follows:
Thus, the particle undergoing simple harmonic motion has following properties:
1- The acceleration of the particle is proportional to the displacement but is in the opposite direction. This is the necessary and sufficient condition for simple harmonic motion, as opposed to all other kinds of vibration.
2- The displacement from the equilibrium position, velocity and acceleration all vary sinusoidally with time but are not in phase. It is shown in the figure as above.
3- The frequency and the period of the motion are independent of the amplitude.
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Waves and Optics