General Forced LCR Oscillator continued

1
General Forced LCR Oscillator (continued)
2
Since we have determined
We can then find the solution
3
So magnitude of transform of current is 1/Z
When imaginary part of impedance Z is zero, the
magnitude of the transform (amplitude of response
to driving voltage at frequency w) reaches a
maximum. This occurs when ww0. The maximum value
is limited by the real part (resistance R).
4
Q-factor and resonance width
If
,
We can represent complex value Z on the complex
plane.
This is where the response is 1/sqrt(2) of its
value at maximum. From our definition of X,
Relative width