Signals and Systems | Impulse Response Problem

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Discussion Overview

The discussion revolves around finding the impulse response for a system described by a differential equation. Participants explore different methods for solving the problem, including the use of Laplace transforms and the homogeneous solution approach.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the problem statement and their initial attempt to find the homogeneous solution for the impulse response, h(t).
  • Another participant requests more detailed work to assist in the solution process.
  • A third participant reiterates the problem statement and suggests changing to the Laplace transform method.
  • A later reply proposes that since the order of x(t) matches that of y(t), the general solution for h(t) can be expressed in terms of the homogeneous solution and a delta function, and mentions using the coefficients equating method to find constants A and B.
  • The same participant claims to have resolved their issue using the Laplace method, indicating satisfaction with their solution.

Areas of Agreement / Disagreement

There is no clear consensus on the best method to solve the problem, as participants suggest different approaches and some express uncertainty about the initial attempts.

Contextual Notes

Some assumptions regarding the initial conditions and the definitions of the functions involved may not be explicitly stated, which could affect the interpretation of the solutions.

Who May Find This Useful

Students or individuals interested in signals and systems, particularly those seeking to understand impulse response calculations and methods for solving differential equations in this context.

haitham111
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Homework Statement


Find the impulse response for the systems governed by the following equations:
3y(t)'+5y(t)=x(t)+x(t)'[/B]

Homework Equations

The Attempt at a Solution



I tried to obtain the homogeneous solution for h(t)[/B]
and then I failed to obtain the coefficients of the solution
 
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you need to show some more work for us to help you. Why don't you show us how you tried to obtain the solution
 
haitham111 said:

Homework Statement


Find the impulse response for the systems governed by the following equations:
3y(t)'+5y(t)=x(t)+x(t)'[/B]

Homework Equations

The Attempt at a Solution



I tried to obtain the homogeneous solution for h(t)[/B]
and then I failed to obtain the coefficients of the solution
Change to Laplace.
 
rude man said:
Change to Laplace.
since the order of x(t) is the same order of y(t)
the general solution of h(t) is h(t)=Ay(t)homo u(t)+Bdelta(t)
and with sub. into the diff.eq i obtained A and B with coefficents equating method.

I tried with laplace, and it had the same answer of the first methodI think my problem is solved right now thank you all
 

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