As you-all know I've been studying pendula, especially WRT Q and amplitude. Horologists claim that increasing the bob mass does not increase the amplitude for constant energy (amplitude) drive. I being stuck on the definition of Q thought no. Increase the bob's mass, and, OTBE, the drive to maintain amplitude will be less or conversely w/ the same drive the amplitude will increase. Whether the drive is harmonic or pulsed and the coupling lose or "tight" the result will be similar.
Now I finally read my "bible" Baker and Blackburn, The Pendulum, a case study in physics and find their formula for the amplitude (harmonically driven) is: Driver amplitude * Q / [mgl * sqrt{1-(1 / 4Q^2) } ] For high Q (good clock pendula Q are > 1000), this reduces to:
the natural angular frequency * driver amplitude / [gl * linear friction constant] Q being m*natural frequency / linear friction constant ***
i.e. the m's cancel. B & B also analyze pulse forcing using the Laplace transform technique and also the Dirac delta function w/ similar to the harmonic forcing result. So I assume the above amplitude equation w/ such drive will be similar. [The small angle and simple (not physical) approximations used thru out.]
So my conclusion is the usual definition of Q is not suitable in the pendulum case, furthermore, a quick, and, therefore, likely deficient, conversion to the spring oscillator also suggests that Q definition is also not suitable there either.
Comments please.
***[ml^2 * theta double dot + gamma* l^2 * teta dot + mgl theta = 0] which reduces to [theta double dot + (gamma / m) theta dot + g / l) theta = 0]