Critical damping provides the quickest approach to zero amplitude

[linyen416]

Critical damping provides the quickest approach to zero amplitude for a damped oscillator. With less damping (underdamping) it approaches zero displacement faster, but oscillates around it. With more damping (overdamping), the approach to zero is slower.

I got this from hyperphysics
but I am not sure aout the last sentence
with more damping shouldn't the approach to zero be even faster

 

[Cyrus]

No, why should it?

 

[linyen416]

cyrus, i thought damping brings it down to zero faster.

also another thing that's troubling me is : for underdamping, overdamping, adn critical damping, do the amplitudes eventually REACH zero IN THEORY or is it that theoretically they only APPROACH zero? thanks

 

[Cyrus]

Well, I would rethink how you came to that conclusion. No where in what you copied from hyperphysics did it says 'damping brings it down to zero faster'.

No, they actually reach zero in physical systems if the system is unforced (meaning there is no energy being supplied). I.e. I give it an intial energy and watch it decay back down to zero - a transient.

If energy is supplied via forcing, its a totally different story. The exact why and how of that is beyond the scope of this thread. For now, just know that if there is an energy input, steady state errors can and do occur in the system. Meaning it won't decay back down exactly to zero -not in theory or in real life.

 

[linyen416]

So for an unforced underdamped oscillation, due to steady state errors that occur in real life, won't decay to zero?

 

[Cyrus]

So for an unforced underdamped oscillation, due to steady state errors that occur in real life, won't decay to zero?

No, re-read what I wrote. I never said any of that. I gave you two clear examples (a) unforced and (b) forced. I have no idea why you took my answer for (a) and applied it to (b)...you need to pay closer attention to what you're reading (both my post and hyperphysics) because you are reading into things that are not being said.

Take a step back and read things for what they are.

 

[linyen416]

cyrus, i was asking abotu unforced underdamped oscillation... so in actual physical systems they do reach zero and but theoretically they dont

 

[linyen416]

wouldn't there be steady state errors in underdamped oscillation that is unforced?

 

[Cyrus]

cyrus, i was asking abotu unforced underdamped oscillation... so in actual physical systems they do reach zero and but theoretically they dont

...I never said that.

Maybe you are not familiar with the term "physical systems" - that means a real system. Its physical.

 

[Cyrus]

wouldn't there be steady state errors in underdamped oscillation that is unforced?

No, there is no energy being supplied to keep it at a nonzero value. So how could it?

 

[linyen416]

theoretically it never reaches zero because of the exponential nature of decay, right?

 

[Cyrus]

theoretically it never reaches zero because of the exponential nature of decay, right?

Yes, that's correct-good observation.