What Went Wrong with My Laplace Circuit Problem?

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SUMMARY

The discussion centers on troubleshooting a Laplace circuit problem where the user correctly identified the denominator but struggled with the numerator due to misinterpretation of circuit sources. The user provided a method for converting Laplace equations to differential equations while ignoring initial conditions, then back to the Laplace domain using specific transform rules. The solution was ultimately found, confirming the effectiveness of this approach in resolving similar issues.

PREREQUISITES
  • Understanding of Laplace transforms and their applications in circuit analysis
  • Familiarity with differential equations and their conversion to Laplace domain
  • Knowledge of initial conditions in the context of Laplace transforms
  • Ability to interpret and redraw circuit diagrams accurately
NEXT STEPS
  • Study the rules for Laplace transforms, particularly for derivatives and initial conditions
  • Learn about circuit analysis techniques using Laplace transforms
  • Explore methods for converting differential equations to the Laplace domain
  • Practice solving circuit problems involving initial conditions and Laplace transforms
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Students and professionals in electrical engineering, particularly those focusing on circuit analysis and control systems, will benefit from this discussion.

NewtonianAlch
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Homework Statement


http://img836.imageshack.us/img836/9994/27794040.jpg

The Attempt at a Solution



Here is the circuit I re-drew:
http://img403.imageshack.us/img403/6752/dsc0048ga.jpg

Working out:

http://img857.imageshack.us/img857/5633/dsc0049mo.jpg

I got the denominator correct, but my numerator isn't. Which means I got something wrong with the sources in the circuit, but I'm not sure where.
 
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It's hard to read your paper. I can only offer you what I do in cases like this where initial conditions exist:

1. Change the Laplace equations to differential equations, ignoring the initial conditions.

2. Change the differential equations back to Laplace domain, using the Laplace transform rules for including initial conditions, e.g.
if F(s) = L{f(t)} then L{f'(t)} = sF(s) - f(0+) etc.

3. Then do the inverse transforms term-by-term.

This is probably equivalent to what you're trying to do, I can't tell.
 
Nvm, solved.
 

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