Relaxation time

In the physical sciences, relaxation usually means the return of a perturbed system into equilibrium. Each relaxation process can be characterized by a relaxation time τ. The simplest theoretical description of relaxation as function of time t is an exponential law exp(-t/τ).

Let the homogeneous differential equation:

model damped unforced oscillations of a weight on a spring.

The displacement will then be of the form ${\displaystyle y(t)=Ae^{-t/T}\cos(\mu t-\delta )}$. The constant T is called the relaxation time of the system and the constant μ is the quasi-frequency.

In an RC circuit containing a charged capacitor and a resistor, the voltage decays exponentially:

The constant ${\displaystyle \tau =RC\ }$ is called the relaxation time of the circuit. A nonlinear oscillator circuit which generates a repeating waveform by the repetitive discharge of a capacitor through a resistance is called a relaxation oscillator.

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