What Mistakes Are Made in Solving Damped Oscillator LCR Circuit Problems?

[pondzo]

Homework Statement

Homework Equations

The Attempt at a Solution

For part (a) i did the following;
the time for it to decay to 40% is half the period of the square wave = 0.00002 seconds
So, 0.4q_m = q_m $e^(\frac{-0.00002R}{2L})cos(25000*2*\pi*0.00002)$
But the cosine term yields -1 which then makes the equation unsolvable, what am i doing wrong?

For part (b) I am a bit confused about the "17 ringing cylcles per half-cycle" but i tried ;

the time for one half oscillation of the square wave voltage is 0.5/(25E3) = 0.00002 seconds
during this time the LCR circuit rings 17 times so the period of oscillation of the LCR circuit is 0.00002/17 = 0.000001176
this corresponds to an angular freq of w = 5340707.511 rad.s^-1
Is this correct so far? and if so, does this mean there will be a different restance in part (b) than in part (a)?

 

[NascentOxygen]

Don't involve the cosine. For the decay all we are concerned with is the exponential envelope.

 

[pondzo]

Thank you, I should have realized that.
Do you know if what i did for part (b) is correct?

 

[NascentOxygen]

Your $\mathrm{\omega}$ looks right. You cannot estimate R from $\textrm{ω}$ because you don't know $\mathbf{ω}$ to the great precision necessary. The exponential decay is what allows you to determine R.