Physics: Basic Resonance Question

Does anyone know what the “Q-factor” is, in relation to vibration, specifically resonance (I do believe)? - Jinx

In general, Q represents the “resistance” of a system to resonance. For a given input, a higher-Q system will resonate with a larger amplitude than a lower-Q one. Q is used to describe mechanical, electrical and optical resonators.

And, if you want an intuitive feel for what the number means, Q is about the number of oscillations a freely-oscillating resonant system will undergo before the oscillations are damped out (i.e., to ~1/e of their original amplitude).

Aye, it’s a measure of the damping factor, where low Q = high damping. I prefer to think of things in terms of damping factor (zeta, where high zeta=high damping) as I can get a clear mental image of what the resonance will look like quite easily.

Q is the ratio of the peak energy stored to the energy lost/cycle at resonance.

For example, in a spring-mass-damper system compute the kinetic energy of the mass at its maximum velocity; compute the energy lost in one cycle in the damper at the resonant frequency. Q is the energy of the mass divided by the damper energy.

Ooops. I forgot the multiplier. The Q is 2π times peak energy stored divided by energy lost/cycle at resonance.

In an RLC electrical circuit, for example, the peak energy stored in the inductor is Li[sup]2[/sup][sub]peak[/sub]/2 and the energy lost/cycle is Ri[sup]2[/sup][sub]rms[/sub]/f. f is the frequency at resonance

Converting the rms current to peak current in the energy lost/cycle term gives Ri[sup]2[/sup][sub]peak[/sub]/2

And if we divide we get 2πfL/R which is the usual formula for Q.

The more I read this the more puzzled I am.

What are you looking for? The Q factor is basically an efficiency indicator. That is, energy stored relative to energy lost. For the designer of a resonant circuit filter, such as the load in an IF amplifier, it defines the bandwidth of the filter. For the communications circuit designer of a bandpass filter it provides an indicator of the insertion loss of the filter. I.e. the designer wants circuit elements with as high a Q as possible so as to have the least loss in the pass band.

And all stuff like that there.