Amplitude

The term amplitude is a term from physics and engineering to describe oscillations. It is related to the physical quantities, such as an AC voltage, and its course over time. In this case, it is defined as the maximum deflection of a sinusoidal alternating quantity from the position of the arithmetic mean. The term is also used for the identification of waves when the oscillation at a constant rate spreads locally ( sine wave).

In DIN 40110-1 distinguishes between

• Peak value of a periodic alternating voltage and
• Amplitude of a sinusoidal alternating voltage.

For other names, which are not limited to changing sizes, but are generally used for periodic processes, such as in mixed voltage, see below peak.

The distance between maximum and minimum is referred to as oscillations with oscillation width or as a peak-to- valley value (formerly known as peak -to-peak value ).

Mathematical representation

An undamped sinusoidal or harmonic oscillation is

Described by the amplitude, angular frequency and zero phase angle. The amplitude is time independent and thus constant.

Another possible description is the complex representation by means of Euler's formula ( with the usual in electrical engineering imaginary unit ).

Only the real part has physical meaning (or the imaginary part ). However, this form simplifies many calculations, see Complex AC circuit analysis. The term

Is the complex amplitude of an amount equal to the amplitude and the argument is equal to the zero phase angle.

In certain contexts, the amplitude can also slow relative to the associated vibration change, such as absorption or modulation.

A weakly damped, non-periodic oscillation with the Abklingkoeffizienten by

Described. The term

Is the time-varying amplitude function.

The targeted modulation of amplitude see amplitude modulation.

Examples

Gladly, the amplitude is illustrated by mechanical examples, especially on the pendulum.

A spring pendulum in the ideal case ( without damping ) of a sine wave. The distance between

• The reversal point in which the pendulum has the largest deflection, and
• The resting point from which the pendulum without energy supply can not perform any vibration,

Is the amplitude.

A planar pendulum still swings even with undamped motion either in the angle sinusoidally in the horizontal deflection. The horizontal distance between the turning point and rest point is a peak value. Only slight deflection, when the peak value is much smaller than the length of the pendulum, that is, when the small angle approximation can be applied, the vibration is sinusoidal, and the peak value is used to amplitude.