Question #927f2
1 Answer
It would be inversely proportional. That's easy to imagine, a system that is damped more will have its fluctuations damped more strongly.
Explanation:
Lets get to the basics, lets start from the basic differential equation describing a damped simple harmonic oscillator.
where
Let us use a trial solution of the form
solving this we get the solution
Let us for a moment assume a oscillatory solution, ie
The complex exponential represents oscillations but the first part represents an decaying exponential. A decaying process is often written in the form
Indeed, as per our intuition the relaxation time is indeed inversely proportional to damping constant. This particular form is particular for an underdamped oscillator, but you can be pretty sure that larger the damping constant, smaller the relaxation time.
Hope this helps!