In physical systems, damping is the loss of energy of an oscillating system by dissipation. Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. Examples of … See more

A damped sine wave or damped sinusoid is a sinusoidal function whose amplitude approaches zero as time increases. It corresponds to the underdamped case of damped second … See more

Using the natural frequency of a harmonic oscillator $${\textstyle \omega _{n}={\sqrt {{k}/{m}}}}$$ and the definition of the damping ratio above, we can rewrite this as: See more

In control theory, overshoot refers to an output exceeding its final, steady-state value. For a step input, the percentage overshoot (PO) is the maximum value minus the step value divided by the step value. In the case of the unit step, the overshoot is just … See more

Depending on the amount of damping present, a system exhibits different oscillatory behaviors and speeds.
• Where the spring–mass system is completely lossless, the mass would oscillate indefinitely, with each bounce of equal height to the … See more

The damping ratio is a parameter, usually denoted by ζ (Greek letter zeta), that characterizes the frequency response of a second-order … See more

The Q factor, damping ratio ζ, and exponential decay rate α are related such that
$${\displaystyle \zeta ={\frac {1}{2Q}}={\alpha \over \omega _{n}}.}$$
When a second-order system has See more