Calculating RLC Circuit Damping Time and Energy Loss

[andrew410]

Electrical oscillations are initiated in a series circuit containing a capacitance C, inductance L, and resistance R.

a) If R << sqrt((4L)/C) (weak damping), how much time elapses before the amplitude of the current oscillation falls off to 50.9% of its initial value?

b) How long does it take the energy to decrease to 50.9% of its initial value?

For part A, since I = I(max) * sin(wt), I put I(max)*.509 = I(max) * sin(wt).
I(max) cancels out and you are left with .509 = sin(wt). I let w = 1/sqrt(LC). Next, I solved for t and came up with t = sqrt(LC)*arcsin(.509). It says the answer is wrong though. Any help would be great! thx! :)

 

[vincentchan]

you were not even answering what the question asked...
for a weak damping oscillation, the amplitude is e^(at)sin(bt) ... whereas a and b are constant...
the question is asking you when will the maximun amplitude i.e. e^(at) decrease to 50.9%, not the whole thing...

 

[andrew410]

so you do .509 = e^(at) and solve for t, where a = -Rt/L?