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

Linear and non linear systems

  1. Feb 18, 2009 #1
    1. The problem statement, all variables and given/known data
    Show that the system is nonlinear:

    y*y' + 3y = x

    2. Relevant equations
    if you multiply y * y' , can you merge the y's together to form y^2(t)'? Thats the only way I see this could be nonlinear.

    Also the input should be of the same form of the output in a linear system right? For example if my input into my system is of x^2, then the output should also be of y^2. But if the input is x^2 and the output is y^4, then this is considered nonlinear correct?

    3. The attempt at a solution

    The book states that for an input x1(t) and x2(t), it should equal the sum of the outputs y1(t) and y2(t). But in the output, the output results in a y^2(t)' , which is not = y(t):

    y1y1' + 3y1 = x1
    y2y2' + 3y2 = x2

    (added together)

    [(y1)^2]' + [(y2)^2]' + 3(y1 + y2) = x1 + x2
  2. jcsd
  3. Feb 18, 2009 #2
    Reattempt at solution

    I forgot that the system is linear if when you add and also multiply by a constant. So if you multiply by a constant it yields this:

    y1k1(y1'k1) + 3y1k1 = x1k1
    y2k2(y2'k2) + 3y2k2 = x2k2

    but noticing before even adding them together, the k1's and k2's multiply each other in the y*y' function resulting in k^2, which is not equal to the k on the input side (the x side). I'm fairly sure this is why its considered nonlinear, but any input would be great. Thanks again.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook