Re: Critical damping of pendulum


JS Groot wrote:
> tadchem wrote:
> >
> > Try this:
> >
http://mathworld.wolfram.com/DampedSimpleHarmonicMotionCriticalDamping.html
>
> Thanks for the link. However, the solution presented there is also
> the one for the linearised differential equation (the 2nd equation in
> my posting), resulting in simple harmonic motion.

"Critical damping" is defined various ways:

Critical Damping: Critical damping is the smallest amount of damping at
which a given system is able to respond to a step function without
overshoot.
(from http://www.flw.com/define_c.htm)

critical damping - damping that just prevents oscillations: damping of
a system that is just enough to prevent oscillations occurring
(from
http://encarta.msn.com/encnet/features/dictionary/DictionaryResults.aspx?refid=561531742)

critical damping - The minimum damping that will prevent or stop
oscillation in the shortest amount of time, typically associated with
oscillatory systems like geophones.
(from
http://www.glossary.oilfield.slb.com/Display.cfm?Term=critical%20damping)

Critical damping is a special case of damped simple harmonic motion in
which (beta)^2 - 4*(omega-0)^2 = 0
(from
http://mathworld.wolfram.com/DampedSimpleHarmonicMotionCriticalDamping.html)

These are all independent of whether the oscillator is linear or
non-linear to the extent that for all non-linear oscillators, small
amplitude oscillations approach linearity so the frequency approaches
that of the linear oscillator.

As the idea of "critical damping" is to reduce the amplitude to 0 in no
more than half a cycle, the non-linearity of the dependence of
frequency upon various parameters does not enter into the problem.

It does not matter whether a large amplitude oscillation takes more
time than a smaller amplitude oscillation, because there is only time
for a half cycle oscillation at best.

What is the 'frequency' of something that is not permitted to repeat?

Tom Davidson
Richmond, VA

.

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