Question

Relation between quality factor and relaxation time

Answer 1

I hope this will help you

Answer 2

Relation between quality factor and relaxation time can be expressed as

$Q=\frac{\tau\omega_{N}}{2}$

• In the above equation, $Q$ is the quality factor, $\tau$ is the relaxation time and $\omega_{N}$ is the natural frequency
• Quality factor (represented as $Q$) is defined as the ratio of stored energy to the energy dissipated over one radian of oscillation.
• Quality factor helps to understand how underdamped an oscillator is.
• If an oscillator has a higher value of Quality factor, it means that there is a lower rate of energy loss and hence the oscillations die out more slowly.
• Relaxation time is described as the time taken to reduce the amplitude of an oscillator to $\frac{1}{e}$ of its initial value.
• Relaxation time is represented by $\tau$
• Natural frequency, $\omega_{N}$, is the frequency at which an oscillator oscillates when there is no damping force