what do you mean by simple harmonic motion
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oscillatory motion under a retarding force proportional to the amount of displacement from a equilibrium position
BhaskarMandal:
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A particle is said to execute simple harmonic motion, if the restoring force acting on it is (1) always directed towards its mean position, and (2) is proportional to its displacement from the mean position.
Suppose a particle is moving along the circumference of a circle of radius A at a constant angular speed w (omega). Let XOX’ and YOY’ be the two diameters of the circle along the X- and Y- axes. Let the position of the circulating particle at time t = 0, be at extreme right end of the horizontal diameter. Let the particle traverse the circumference in an counter-clockwise sense. From the position of the particle on the circumference, imagine perpendiculars drawn on the horizontal diameter. As the particle revolves at constant angular speed, the foot of the perpendicular from its position on the circumference on to the horizontal diameter, executes a simple harmonic motion. The to and fro motion of the foot of the perpendicular, is a SHM. The time period of the simple harmonic motion is the time taken by the particle to complete, one revolution of the circumference. Since the angular speed of the particle is w, the time period of SHM is T = 2π/w.
So SHM is periodic. But so is the motion of the particle revolving around the circle. But motion of the particle is not Simple Harmonic. It is the foot of the perpendicular which is undergoing SHM
So whereas all simple harmonic motion is periodic, not all periodic motion is simple harmonic.
Suppose a particle is moving along the circumference of a circle of radius A at a constant angular speed w (omega). Let XOX’ and YOY’ be the two diameters of the circle along the X- and Y- axes. Let the position of the circulating particle at time t = 0, be at extreme right end of the horizontal diameter. Let the particle traverse the circumference in an counter-clockwise sense. From the position of the particle on the circumference, imagine perpendiculars drawn on the horizontal diameter. As the particle revolves at constant angular speed, the foot of the perpendicular from its position on the circumference on to the horizontal diameter, executes a simple harmonic motion. The to and fro motion of the foot of the perpendicular, is a SHM. The time period of the simple harmonic motion is the time taken by the particle to complete, one revolution of the circumference. Since the angular speed of the particle is w, the time period of SHM is T = 2π/w.
So SHM is periodic. But so is the motion of the particle revolving around the circle. But motion of the particle is not Simple Harmonic. It is the foot of the perpendicular which is undergoing SHM
So whereas all simple harmonic motion is periodic, not all periodic motion is simple harmonic.
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