Note on the value of "Q"

One way to define the "Q" factor for a damped oscillator is by counting the number of cycles it takes for the amplitude to decay significantly. The general rule is



     low Q system           amplitude decays to 1/e in a few cycles

     high Q system          amplitude decays to 1/e only after many cycles

That's certainly true.

One can make a more quantitative statement, as shown in the lecture on forced harmonic motion. Specifically,

From which one can derive an almost-simple way of calculating Q.

Unfortunately, in the review session just before Test 1, I got it wrong: I stated, and wrote on the board, that Q was equal to the number of cycles required to decay to (1/e) divided by π, instead of (1/e) multiplied by π.

Please accept my apologies. Before we move on, please take the time to check your notes, and, if necessary, to correct them.