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 Laplace transforms to solve differential equations - with a twist!

  1. Sep 21, 2014 #1
    I've been given this:
    x''+ x = 4δ(t-2π)

    The question asks:
    With initial conditions of x(0) = 1 and x'(0) = 0, find x(t) using Laplace transforms.

    I can easily get it to this:


    But the question says "express your final solution without use of the unit step function". This is where I get confused as I'm not quite sure as to how to do that. Will it just be 4sin(t)? Considering the sin function repeats at 2π.
  2. jcsd
  3. Sep 22, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    In general if you have ##x=f(t)u(t-a)## you would write a two piece function since ##u(t-a) = 0## if ##t<a## and ##u(t-a) = 1## if ##t>a##. So you would say$$
    x =\left\{\begin{array}{l}
    \end{array}\right.$$Does that help?
  4. Sep 22, 2014 #3
    That's what I was thinking but I was wondering if there was another way of transforming it at all? Seems to simple of an answer for this specific lecturer who wrote the question.
  5. Sep 22, 2014 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Your answer isn't correct. Did you forget to incorporate the initial conditions?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted