How much resistance must be added to a pure LC circuit (L = 340 mH, C = 2200 pF) to change the oscillator's frequency by 0.10 percent?
Will the frequency be increased or decreased?
I'm assuming critical damping: R^2=4L/C, w=((1/LC)-R^2/(4L^2))^1/2
With no R: w=(1/(LC))^1/2
The Attempt at a Solution
I've been at this for a few hours :/ I'm letting w stand in for frequency since w=2pif the percent change needed for f should be the same for w (I hope). I've tried several approaches:
First, I tried w=(1/LC)^1/2 to get w. Then multiplied w by .001 to get .1%. Then made an equation: w-((1/LC)-R^2/(4L^2))^1/2=.001w
That didn't work, but the answer was close to the given one.
I also tried simply setting .001w=(1/LC-R^2/2l^2)^1/2 and that answer was further off.
If I'm missing anything or you need information I'd be happy to give it I'm really enthusiastic to get this done. Thank you in advance!