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Color_of_Cyan

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- Homework Statement
- For a circuit, applying Laplace transform, the output is related to input by:

V_o(S)=(N(s) V_i(s) - s^2+s-2)/D(s),

where D(S) = (s^3 + s^2 + 1).

Find ALL initial conditions (there is no need to know N(s) ).

- Relevant Equations
- Partial Fraction Expansion, Laplace Transforms:

d^n x(t) / dt^n <---> s^n X(S) - s^n - 1x(0-) – s^(n-2)x'(0-) – s^(n-3)]x''(0-) ….

dx(t)/dt <---> sX(s) – x(0-)

d^2x(t)/dt^2 <---> s^2X(s) – sx(0-) – x/(0-)

Vo(S) = [ N(s)V

can ignore (-s^2 + s - 2).

From relevant equations:

Vo(S) = [N(s)*Vi(s)]/(s^3 + s^2 + 1); -> (d

L[vi(t)] = t to s domain: [s

= [s

I'm sort of lost simplifying this now. I know I'm supposed to set up for partial fraction expansion eventually but not sure how.

_{i}(s) + (- s^{2}+ s - 2) ] / s^{3}+ s^{2}+ 1 ;can ignore (-s^2 + s - 2).

From relevant equations:

Vo(S) = [N(s)*Vi(s)]/(s^3 + s^2 + 1); -> (d

^{3}V_{o}(t)/dt^{3}) + (d^{2}V_{o}(t)/dt^{2}) + Vo(t) = N(t)(dvi)/dtL[vi(t)] = t to s domain: [s

^{3}V_{o}(s) - s^{2}V_{o}(0-) - SV'_{o}(0-) - V_{o}''(0-)]V_{o}(s) + s^{2}- SV_{o}- V'_{o}(0)] V_{o}(s) + V_{o}(s) = N(V_{i})(s)= [s

^{3}V(s) - s^{2}+ s + 2] V_{0}(s) + [s^{2}- s - 1]V_{0}(s) + V_{0}(s) = N(V_{i}(s))I'm sort of lost simplifying this now. I know I'm supposed to set up for partial fraction expansion eventually but not sure how.