S-domain analysis with initial conditions

[jisbon]

Homework Statement

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Relevant Equations

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I've attempted this questions after understanding the theory from my lecture notes, but my equation is looking bizarre here. Is this correct so far?

Are my mesh equations correct here?
Thanks.

 

[gneill]

Hi @jisbon,

What's this voltage source all about?

At steady state (t = 0^-) there's no current through the inductor, so it shouldn't require an "initial condition" source.

My first instinct would be to reduce the voltage source and resistors to their Thevenin equivalent before writing loop equations. That'd reduce your $t > 0$ circuit to a single loop (and hence a single equation):