What exactly are frequencies

Amplitude, period of oscillation, frequency

Sine curve of a harmonic oscillation

The graphic above shows the sine curve of an undamped harmonic oscillation. This graphic is intended to describe some variables that apply to every oscillation:

  • The Deflection $ y (t) $ in $ y $ direction (also becomes Elongation called) shows the momentary Distance of the body from the resting position. The deflection can be specified in the positive or negative $ y $ direction.

  • The amplitude is the amount of the maximum deflection in the $ y $ direction. In the case of harmonic undamped oscillation, the amplitude is constant, i.e. the distance from the rest position is the same for both reversal points.
  • The Oscillation period $ T $, indicates how much time the vibrating body needs for a back and forth movement. The unit of the period of oscillation is seconds:
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Unit: 1s [second] period of oscillation $ T $


Often the frequency $ f $ of an oscillation is specified instead of the oscillation period $ T $. The frequency is the reciprocal of the period of oscillation and indicates the number of oscillations that a body has in a certain time $ t = T $:

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$ f = \ frac {1} {T} $ frequency

The unit of frequency is Hertz (Hz), which was named after Heinrich Hertz.

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Unit: $ \ frac {1} {s} = Hz $

If, for example, a frequency of 1 Hz is given, exactly one oscillation process takes place in one second.