Simple Harmonic Motion
The simplest possible vibratory motion that can exist is the movement in one direction of a mass controlled by a single spring. Such a mechanical system is called a single degree of freedom spring-mass system. If the mass is displaced a certain distance from the equilibrium point and then released, the spring will return it to equilibrium, but by then the mass will have some kinetic energy and will overshoot the rest position and deflect the spring in the opposite direction. It will then decelerate to a stop at the other extreme of its displacement where the spring will again begin to return it toward equilibrium. The same process repeats over and over with the energy sloshing back and forth between the spring and the mass -- from kinetic energy in the mass to potential energy in the spring and back.
The following illustration shows a graph of the displacement of the mass plotted versus time.
If there were no friction in the system, the oscillation would continue at the same rate and same amplitude forever. This idealized simple harmonic motion is almost never found in real mechanical systems. Any real system does have friction, and this causes the amplitude of vibration to gradually decrease as the energy is converted to heat. The following definitions apply to simple harmonic motion:
T = The period of the wave.
The period is the time required for one cycle, or one "round trip" from one zero crossing to the next zero crossing in the same direction. The period is measured in seconds, or milliseconds, depending on how fast the wave is changing.
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The unit for frequency is the Hz, named after Heinrich Hertz, the German scientist who first investigated radio.
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F = The Frequency of the wave, = 1/T The frequency is the number of cycles that occur in one second, and is simply the reciprocal of the period. |
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