Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] Oscillator amplitude(Q) question.




On 2011, May 08, , at 16:15, brian whatcott wrote:

On 5/8/2011 5:07 PM, Bernard Cleyet wrote:


cut



Is this what you were hoping for?


Nope. What I hoped was a discussion on the general relationship of Q
and amplitude of a driven harmonic oscillator at resonance.
Both mechanical and electric (RCL).

Hint: Does increasing the Q result in increased amplitude, always?


bc has given up and given it away.

p.s. for pendula, horologists have known (experimentally) the answer
to this for centuries.
The answer is obvious from the particular solution of the inhomogenous
diff. eq.

It's amusing to suppose that the maker of the World's most accurate
chronometer design of its day, or the maker of the World's most accurate
observatory pendulum clock design of its day would have considered
differential equations in the design of their respective
masterworks.

I wrote experimentally.


Amusing, but inaccurate.

But getting back to bc's puzzlement: one can provide increased amplitude
for a mechanical or electrical oscillator with higher, same or lower Q
than before.
Is that plain enough? :-)


Sure by changing the amplitude of the drive.

I, obviously, was not clear. Assume constant drive at the natural frequency so the system is in resonance and the amplitude is maximum. Under these conditions what is the relationship of the amplitude and the Q of the oscillator(s).

bc


Brian W