Hello, I need some help on a laplace circuit problem. Here is the circuit
As you see I added a 10 volt voltage source to represent the initial charge on the capacitor. Then I drew the equivalent laplace circuit representing the impedance of the capacitor and inductor in terms of S.
The object here is to find the current I(t) in the mesh.
So I write KVL.
Now to guess at the solution, I check the poles by setting the denominator = 0.
I get the following. S1= -200 plus 400 j S2= -200 minus 400 j
So the solution should be of the form A e^-200t sin(400t) + B e^-200t cos(400t) or so I remember from differential equations class.
So now I need to do partial fractions. Okay in my book I have this equation.
My question is, how do I use that equation or ANYTHING ELSE to get the inverse laplace of my expression for i(s) above?
The book says the answer is
i(t)= -1/40 e^-200t *sin(400t)
So I know for sure that my expression for i(s) is correct. How do I get i(t) though. Please help. I am having real trouble with complex conjugate pairs in laplace circuits.
As you see I added a 10 volt voltage source to represent the initial charge on the capacitor. Then I drew the equivalent laplace circuit representing the impedance of the capacitor and inductor in terms of S.
The object here is to find the current I(t) in the mesh.
So I write KVL.
Now to guess at the solution, I check the poles by setting the denominator = 0.
I get the following. S1= -200 plus 400 j S2= -200 minus 400 j
So the solution should be of the form A e^-200t sin(400t) + B e^-200t cos(400t) or so I remember from differential equations class.
So now I need to do partial fractions. Okay in my book I have this equation.
My question is, how do I use that equation or ANYTHING ELSE to get the inverse laplace of my expression for i(s) above?
The book says the answer is
i(t)= -1/40 e^-200t *sin(400t)
So I know for sure that my expression for i(s) is correct. How do I get i(t) though. Please help. I am having real trouble with complex conjugate pairs in laplace circuits.