1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Using Stepfunction to solve IVP

  1. Oct 25, 2009 #1
    1. The problem statement, all variables and given/known data

    I am given the task for finding the laplace transformation given

    [tex]y'' + 4y = 8t^2 [/tex] if 0<t<5 and 0 if t>5 y(1) = 1+cos(2) [tex]y'(1)= 4-2sin(2)[/tex]

    2. Relevant equations

    3. The attempt at a solution

    I know that the above problem can be written [tex]y''+4y=8 \cdot u(t)[/tex]

    where u(t) is the step function.

    But what is my next step?

    [tex]\mathcal{L}(y''+4y) = \mathcal{L}(8t^2)[/tex]

    which equals

    [tex]\mathcal{L}(y'') + \mathcal{L}(4y) = 8\mathcal{L}(t^2)[/tex]

    [tex]\mathcal{L}(y'') = s \cdot \mathcal{L}(y') - y'(1) [/tex]

    [tex]\mathcal{L}(y') = s \cdot \mathcal{L}(y) - y(1) [/tex]

    not sure what to do about the left side by the rightside that is [tex]Y(s^2+ 4) = \frac{16}{s^3} + s(1+cos(2)) + (4-2sin(2)) [/tex]

    then [tex]Q(s)= \frac{1}{s^2+4}[/tex]

    then [tex]Y(s) = s(1+cos(2)) + 4-2sin(2)) \cdot \frac{1}{s^2+4} + \frac{16}{s^3} \cdot \frac{1}{s^2+4}[/tex] Is this true or am I totally fubar?
    Last edited: Oct 25, 2009
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted