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: How to solve this problem using laplace transform?

  1. Nov 17, 2015 #1
    1. The problem statement, all variables and given/known data
    The differential equation given:

    2. Relevant equations

    3. The attempt at a solution
    I used the laplace transform table to construct this equation,and then I did partial fraction for finding the inverse laplace transform.But I'm now stuck at finding the inverse laplace transform of 1/s^3 and 1/s^2...

    And the attached photo is the attempted solution.
    View attachment 92000

    Attached Files:

  2. jcsd
  3. Nov 17, 2015 #2


    Staff: Mentor

    I didn't verify your work, but here is a table of Laplace transforms - http://web.stanford.edu/~boyd/ee102/laplace-table.pdf
  4. Nov 18, 2015 #3
  5. Nov 18, 2015 #4


    Staff: Mentor

    Look just below the one for 1/s2. It's a more general formula.
  6. Nov 18, 2015 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    If you know the inverse transform of 1/s, then you can get the inverse transform of 1/s^2 by integration, and of 1/s^3 by integration again. Remember: there are some standard general transform results that are helpful. Below, let ## f(t) \leftrightarrow g(s) = {\cal L}(f)(s)##. Then:
    [tex] \begin{array}{l} \displaystyle \frac{df(t)}{dt} \leftrightarrow s g(s) - f(0+)\\
    \int_0^t f(\tau) \, d \tau \leftrightarrow \displaystyle \frac{1}{s} g(s)
    These were given specifically in the table suggested by Mark44; did you miss them?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted