Laplace and differential equation problem.HELP

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SUMMARY

The discussion revolves around deriving a differential equation from a given transfer function H(s) = (s + 1) / (s(s + 1) + 1). The user seeks assistance in converting the transfer function back to its corresponding differential equation that relates the input u(t) and output w(t). Key steps include multiplying the output w(t) by the denominator and the input u(t) by the numerator of the transfer function. The user successfully derived a differential equation but awaits confirmation of its correctness from their teacher.

PREREQUISITES
  • Understanding of transfer functions in control systems
  • Familiarity with Laplace transforms and their properties
  • Knowledge of differential equations and their applications
  • Basic concepts of system dynamics and input-output relationships
NEXT STEPS
  • Study the derivation of differential equations from transfer functions
  • Learn about the properties of Laplace transforms, specifically inverse transforms
  • Explore examples of system dynamics in control theory
  • Investigate the application of differential equations in engineering problems
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Students in engineering or applied mathematics, particularly those studying control systems and differential equations, will benefit from this discussion.

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Homework Statement



I have this parallel system and i have found its transfer function.Now i have to find what is the differential equation that links the input and the output

Homework Equations



u(t)=input, w(t)=output H(s)=w(s)/u(s)=s+1/s(s+1)+1 -->transfer function

The Attempt at a Solution



I think i have to go backwards starting from H(s) but i don't know how to do it

Any help?
 
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Multiply w by the denominator and u by the numerator of the TF.
Remember that the inverse transform of sF(s) is [tex]\frac{df}{dt} - f(0^-)[/tex] and that of [tex]s^2F(s)[/tex] is [tex]\frac{d^2f}{dt^2} - \frac{df}{dt}(0^-) - f(0^-)[/tex].
 
Thank you.I did it and i found a DE. Don't know yet if it is correct,though.I will tell you as soon as my teacher grades my paper.Thank for the help,though. I really appreciate it.
 

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