Omega Used
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When s is replaced by jw (j omega) in a circuit equation, I could have used phasors to get the result... ?
So why use Laplace? Is is impossible to do second order systems with phasors or somethings?
Normally you use a Lapace transformation to solve for the transient condition (initial startup, reaction to a unit step or impulse, etc.), while you use a Fourier transform to solve for the steady-state condition.
Phasors only work in the steady-state condition where the excitation is a single-frequency sine-wave (with phases, thereof).
For any other repetitive waveshape (square wave, triangle, sawtooth, etc.) Fourier works in the steady state, whereas phasors won't (because of harmonics).
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