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!

Laplace transform of sin(2t)cos(2t)

  1. Mar 18, 2009 #1

    JJBladester

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data

    Find the Laplace transform of

    f(t) = sin(2t)cos(2t)

    using a trig identity.


    2. Relevant equations

    N/A.

    3. The attempt at a solution

    I know the double-angle formula sin(2t) = 2sin(t)cos(t) but that's not helping much. Can you give me some advice on how to proceed.
     
  2. jcsd
  3. Mar 18, 2009 #2
    Consider that

    [tex]\sin{(4t)}=2\sin{(2t)}\cos{(2t)}[/tex]
     
  4. Mar 19, 2009 #3

    JJBladester

    User Avatar
    Gold Member

    Okay, then [tex]\sin{(2t)}\cos{(2t)} = 1/2\sin{(t)}\cos{(t)}[/tex]

    The Laplace integral is then:

    [tex]1/2\int{e^{-st}\sin{(t)}\cos{(t)}}dt[/tex]

    So where do I go from here to solve this? The [tex]e^{-st}[/tex] is throwing me off, otherwise I'd just do a u substitution with [tex]u = \sin{(t)}[/tex] and [tex]du = \cos{(t)}dt[/tex].
     
  5. Mar 19, 2009 #4
    Well if you have that

    [tex]\sin{(4t)}=2\sin{(2t)}\cos{(2t)}[/tex]

    then

    [tex]\sin{(2t)}\cos{(2t)}=\frac{1}{2}\sin{(4t)}[/tex]

    So then if you want to do it from the integral you just need to integrate

    [tex]\int_0^{\infty}\frac{1}{2}\sin{(4t)}e^{-st}dt[/tex]

    where the [itex]s[/itex] you treat as a constant (you're integrating with respect to [itex]t[/itex]). But you could just use the known laplace transform for [itex]\sin{(at)}[/itex] unless you are meaning to derive it.
     
  6. Mar 19, 2009 #5

    JJBladester

    User Avatar
    Gold Member

    Ahhhh lights coming on. Thanks for the help!
     
  7. Mar 19, 2009 #6
    Ah good--glad to help.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Laplace transform of sin(2t)cos(2t)
  1. Sin(t) cos(2t) = ? (Replies: 3)

Loading...