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RLC second order linear network question:

So, we are given this equation which is the same for Vc(t) and iL(t) expressed as x(t):

2nd deriv of x(t) + R/L(1st deriv of x(t)) + 1/(LC)(x(t)) = 0;

And in one of the problems it asks to find both equation for the Vc(t) and iL(t) for t < 0, and now I am confused, it seems to me that they are the same, since the solution is the same for both of them:

aS^2 + bS + c = 0;

because the coefficients are the same from differential equation, so there are the same roots for Vc(t) and iL(t), and roots are w/t imaginary part, just reals.

Am I wrong?

Thanks a lot.

So, we are given this equation which is the same for Vc(t) and iL(t) expressed as x(t):

2nd deriv of x(t) + R/L(1st deriv of x(t)) + 1/(LC)(x(t)) = 0;

And in one of the problems it asks to find both equation for the Vc(t) and iL(t) for t < 0, and now I am confused, it seems to me that they are the same, since the solution is the same for both of them:

aS^2 + bS + c = 0;

because the coefficients are the same from differential equation, so there are the same roots for Vc(t) and iL(t), and roots are w/t imaginary part, just reals.

Am I wrong?

Thanks a lot.

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