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Confused about unit step function wrt laplace transforms

  1. Mar 18, 2012 #1
    1. The problem statement, all variables and given/known data
    y'' + 4y' + 2y = u_pi(t) + u_2pi(t)
    y(0) = 0 and
    y'(0) = 0.


    2. Relevant equations
    the step function equation:
    u_c(t) = u(t-c) --> (laplace) --> e^-cs/s


    3. The attempt at a solution
    i am having major probs with getting my head around step function probs wrt laplace transforms. What would be really really helpful if someone could just explain really simply what is going on with these sorts of problems, with particular emphasis on the notation used and how an equation (like the one above can be graphed. (for example, does the pi in u_pi mean "when t=pi" ?)

    Heres what I do know (or think i know)
    I know what a step function looks like when its graphed and that they are described like
    f(t) = 1 0<t<1
    = 0 1<t<2
    (also, I am ok with taking the laplace or inverse laplace of functions)

    the main problem im having is with the notation used, (u_2pi for example) and specifically how an equation such as the one above is graphed?
    But if you dont want to explain anything, then if I can get thru this problem i think i will understand whats going on, so if you can give any hints or anything on how to start a problem like this..thanks alot!
    thanks for any help
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 18, 2012 #2
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