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I am WEAK in DE's. I have been trying to understand this question all day. I posted the question as an image since I don't have enough rep points to post it here.

There is one example in my text Butkov on how to do this but it is not clear at all to me what I must do!

so far I just wrote:

L* i"(t) + R* i'(t) + (1/C) i(t) = -Vo*ω*sin(ω*t)

I then took a function f(t) = F*exp(i*t)

where F = Vo*ω, and so F*exp(i*t) = Vo*ω(cosωt - i*sinωt)

I then wrote im{Vo*ω*exp(-it)} = -Voωsinωt

I clearly have no idea what I am doing. Please, any help would be appreciated.

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The link isn't working for me. – Gerry Myerson Jan 24 '12 at 23:47
My apologies. I reposted it on Photobucket. Perhaps this website restricts certain urls.… – user23463 Jan 24 '12 at 23:59

You're trying to solve the differential equation $L i''(t) + R i'(t) + (1/C) i(t) = - V_o \omega \sin(\omega t)$. The right side is the imaginary part of $- V_o \omega e^{i\omega t}$, so the idea is to first find a solution of the differential equation with right side replaced by $-V_o \omega e^{i\omega t}$, and the imaginary part of that solution will be a solution of your differential equation. Try a solution of the form $y(t) = A e^{i\omega t}$: plug this in to the (new) differential equation, and see if you can find a complex constant $A$ that makes the equation true.

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