Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear systems

  1. Aug 15, 2007 #1
    how can i prove mathematically if a system is linear or not? i mean, i know the system must obey proportionally law and superpositon, but i dont know how apply into it.
    well, if anyone could help me, the systems i need to prove are:
    x(t) -> y(t)= Cx(t) + k
    x(t) -> y(t)= ∫ (from minus infinite to "t") x(e)d(e); where "e" is a dummy variable
     
  2. jcsd
  3. Aug 19, 2007 #2
    look if i/p x(t) is scaled by a1, then
    o/p is y1(t)=a1*Cx(t)+k

    if scaled by a2 it becomes
    y2(t)=a2*Cx(t)+k

    now to obey linearity if i/p is a1*x(t)+a2*x(t), then o/p should be
    y(t)=y1(t)+y2(t)

    but in this case if i/p is a1*x(t)+a2*x(t)
    y(t)=a1*Cx(t)+a2*Cx(t)+k

    which is not equal to
    y1(t)+y2(t)= a1*Cx(t)+a2*Cx(t)+2k

    So this sys is not linear
     
  4. Aug 19, 2007 #3
    Sorry made mistake

    Sorry made a mistake there it should have been

    if i/p is x1(t) , then
    o/p is y1(t)=Cx1(t)+k

    if i/p is x2(t) it becomes
    y2(t)=Cx2(t)+k

    now to obey linearity if i/p is a1*x(t)+a2*x(t), then o/p should be
    y(t)=a1*y1(t)+a2*y2(t)

    but in this case if i/p is a1*x(t)+a2*x(t)
    y(t)=a1*Cx(t)+a2*Cx(t)+k

    which is not equal to
    a1*y1(t)+a2*y2(t)= a1*Cx(t)+a2*Cx(t)+(a1+a2)k

    So this sys is not linear:redface:
     
  5. Aug 20, 2007 #4
    Thank u, I finally got the right result...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?