Harmonic oscillations

Harmonic oscillations . They constitute a periodic phenomenon , in which the variation of the observed magnitude obeys the sine law or the cosine law.


The projection of a point that moves with uniform circular motion, on a line that is in the plane of motion (figure # 1) varies with time according to a sinusoidal law . If the circumference has radius R and the angular speed of rotation of the point is w, the projection x is:

Obviously the period of variation of x is:

At the end of time T, that is, the time of one revolution of the point, the entire process will be repeated exactly. Therefore T is called the period of the harmonic oscillations, and w, the circular (or cyclical) frequency of the harmonic oscillations. The number of oscillations per unit of time is called the frequency of the oscillations .

The frequency is measured in hertz (Hz). Harmonic motion is frequently found when a uniform rotational motion occurs, however, the motion of a steam engine or internal combustion engine piston, the motion of evenly rotating the flywheel, are not pure harmonic motion; these periodic movements only resemble harmonics under certain conditions.
The given description of this phenomenon only corresponds to the kinematics of the movement, the physical conditions under which this movement is studied corresponds to the dynamics


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