Solve Electrical Circuit Problem: Particular Solution

[palaszz]

Hi everybody. I've got kind of a problem solving the following problem, so really hope for some help. The task says:

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The figure beneath shows an electrical circuit containing following components: a resistance R, a capacitor with the capacitance C and finally a voltagegenerator E with the voltage E(t)=cos(2t).

http://img573.imageshack.us/img573/7493/matafl4.jpg

Now the voltage can obviously be determined by this diff.equation:

- R*C*(dV(t)/dt)+V(t)=cos(2t).

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Now my problem is to - with help from the complex guessing-method - to determine a particular solution for the differential equation, and to make use of this in order to give the total solution of the differential equation.

Furthermore, in which way will it impact the circuit if I make use og this particular solution and at the same time make R=1 and C=1 and V(0)=2 ?

Really hope that someone can help me getting started.

 

[Office_Shredder]

When you have a differential equation and it equals a function of t, usually that's where you want to start your guess.

So you have diff. eqn=cos(2t) here. Which means that in V(t) and dV/dt we are going to need cos(2t) . So start your guess with V=Acos(2t) where A is an arbitrary constant. Then we get Acos(2t)+2RCAsin(2t)=cos(2t). This requires A to be 0 and 1 simultaneously, so there's no solution. The key is to add on new functions to our guess. Do you see what we want our next guess to be?

 

[LCKurtz]

Note that you don't even need to use that method. Your equation can be rewritten in the form

V'(t) + kV(t) = k*cos(2t)

This is a linear equation with integrating factor e^kt, so multiply both sides by that and you will have an exact derivative to integrate.