Laplace and transfer function ( input output voltage)

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SUMMARY

The discussion centers on solving a transfer function problem involving the convolution integral. The transfer function is given as H(s) = Vo/V1 = (10/s)/(4 + 0.4s + (10/s)), with the input voltage V1 defined as V1 = 10(u(t) - u(t - 0.1))V. Participants emphasize the necessity of finding the impulse response in the time domain before applying the convolution integral, rather than working solely in the Laplace domain, which complicates the inversion process.

PREREQUISITES
  • Understanding of transfer functions and their representation.
  • Familiarity with convolution integrals in signal processing.
  • Knowledge of Laplace transforms and their applications.
  • Ability to interpret and manipulate unit step functions, such as u(t).
NEXT STEPS
  • Study the derivation of impulse responses from transfer functions.
  • Learn the application of convolution integrals in time-domain analysis.
  • Explore techniques for Laplace transform inversion, particularly for complex functions.
  • Review examples of multiple choice questions involving transfer functions and convolution.
USEFUL FOR

Students in electrical engineering, control systems, or signal processing who are tackling transfer function problems and convolution integrals in their coursework.

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Homework Statement


Given transfer function : H(s)=Vo/V1=(10/s)/(4+0.4s+(10/s)) and the input voltage is given as V1=10(u(t)-u(t-0.1))V. Use the convolution integral to find Vo for t>=0.1


Homework Equations


convolution integral..its hard to write and laplace table

The Attempt at a Solution


find the laplace for v1 then find laplace for Vo which is the transfer function times V1.. however when I'm doing that I am getting an extremely hard laplace to invert.
This should not be the case since this is a multiple choice question of an exam i had today
Thank you a lot
 
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The problem tells you to use the convolution integral, so I have no idea why you are working in the Laplace domain. Your first step should be to find the impulse response in the time domain.
 

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