Damped Harmonic Oscillator

[Sarah Mehar]

Following is a question from a past paper

"Write the equation of Damped Harmonic Oscillator and discuss all three conditions of damping."

I cannot find the three conditions of damping in the recomended books. The genral equation of damped oscillator has been explained in the recomended books.
After some net surfing I dug out the 3 conditions of damping with little explanation, but without derivation.

Now I want to ask, if this question is asked again then do i need detailed derivation of all 3 conditions or derivation of genral equation and some explanation of 3 conditions will suffice the need?

Dear members please share your view and do mention some source from where I can find derivation of 3 conditions of damping (if it is required).

[civilengineer92]

As far as i remember, the three conditions are underdamped, overdamped & critically damped and they don't have any derivation but a graph b/w distance and time depicting them collectively. You would need a bit explanation of the case in the light of equation for each case i-e b/2m < Wo in case of underdamped, b/2m > Wo for overdamped and equal for critically damped (i may be wrong so proof check these equations) just a 8-10 line explanation for each case with a collective graph will suffice.

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