Simple step function, Laplace transform

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SUMMARY

The discussion centers on solving a differential equation characterized by y' + 3y = r', where the input r(t) is defined as u(t) - u(t-1). The solution involves finding y(t) through the inverse Laplace transform of Y(s), utilizing the transfer function Q = s/(s+3) and the impulse response qimp(t) = δ(t) - 3e^(-3t). The participant initially expressed confusion but successfully arrived at the solution.

PREREQUISITES
  • Understanding of differential equations
  • Familiarity with Laplace transforms
  • Knowledge of transfer functions
  • Basic concepts of impulse response
NEXT STEPS
  • Study the properties of the Laplace transform in detail
  • Learn how to derive transfer functions from differential equations
  • Explore the concept of impulse response in linear systems
  • Practice solving differential equations using the Laplace transform method
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Students and professionals in engineering, particularly those focusing on control systems and signal processing, will benefit from this discussion.

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Homework Statement


A system is characterized by the equation y' + 3y = r' .

When the input is r(t) = u(t) - u(t-1), find y(t) by taking the inverse Laplace transform of Y(s).

Homework Equations


The Laplace transform integral
The Laplace transform of a derivative sF(s) - f(0)

The transfer function of the system Q = s/s+3

The impulse response qimp(t) = δ(t) - 3e-3t

The Attempt at a Solution


I'm really not sure what to do here. It seems like it should be simple enough but I feel like I am not understanding the question correctly. Any hints?
 
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Nevermind, got it.
 

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