Question

What is the formula for damping factor?

Answer 1

Hint:Damping is an impact within or upon an oscillatory system that decreases or prevents oscillation. In physical systems, damping is generated by processes that waste the energy stored in the oscillation. Examples involve
viscous drag in mechanical systems,
resistance in electrical oscillators, and
scattering and absorption of light in optical oscillators.

Complete step-by-step solution:
The damping ratio is a dimensionless quantity describing how vibrations in a system decay after a change. Many systems display oscillatory behaviour when they are displaced from their static equilibrium position. A mass hung from a spring, for example, might, if drawn and released, jump up and down. On each bounce, the system manages to return to its equilibrium state but overshoots it. Sometimes damages damp the system and create the oscillations to decay in amplitude towards zero or attenuate gradually. The damping ratio is an estimate describing how rapidly the vibrations decay from one bounce to the following.
The damping factor is a parameter of the system, expressed by b, that can differ from undamped ($b = 0$ ), underdamped ($b < 1$ ) through critically damped ($b = 1$ ) to overdamped ($b > 1$).
The damping factor is the critical parameter related to resonant circuits. It can be denoted as b. It measures the rate of reduction of oscillations when the source is eliminated and can be measured using the formula:
$W = W_{o} e^{-2bt}$
Where $W_{o}$ is the energy present in the system at $t=0$ .

Note:Damping, which is not based on energy loss, can be necessary for other oscillating systems such as those that happen in biological systems and bikes. Not to be mixed with friction, which is a dissipative force operating on a system. Friction can produce or be a factor of damping.