Question

Consider an LC circuit in which L = 490 mH and C = 0.108 µF.

(a) What is the resonance frequency ω₀?
4.35 krad/s

(b) If a resistance of 1.08 kΩ is introduced into this circuit, what is the frequency of the damped oscillations?
4.20 krad/s

(c) By what percentage does the frequency of the damped oscillations differ from the resonance frequency?
-3.448 %

The first two are correct, the last one is incorrect. I get this response:

Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.%

Can someone please explain how to do part c?

Answer 1

(A) w0 = 1/ sqrt(LC) = 4347 rad/s

(B) w = sqrt[ 1/LC - R^2 / 4L^2]

w = 4205 rad/s

(C) % = ( (w0 - w) / w0) x 100

= ( ( 4347 - 4205) / 4347) x 100

= 3.27 %

{ only three significant figures have to use to only as in every given value there are only three significant values}