We note that each differentiation in time has been replaced by a multiplication by (j
ω
)
in the equation determining the complex amplitude in the assumed particular solution. Once
we appreciate this point, we can straightaway obtain the equation governing the complex
amplitude A of the steady-state response to a complex exponential input by replacing every
differentiation in the differential equation by a multiplication by j
ω
and solve for A easily.
Let us generalise this. We consider a linear circuit with one sinusoidal source at an
angular frequency of
ω
driving it. If there are more sources, we employ the superposition ...
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