Results 1 to 8 of 8

Math Help - Laplase Transformations! Please save me from this problem!

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    19

    Laplase Transformations! Please save me from this problem!

    Find the laplace transformation of the following:
    I don't even know where to start< please Help>
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Bananna View Post
    Find the laplace transformation of the following:
    I don't even know where to start< please Help>
    I have some thoughts but I don't have time right now. If no-one else jumps in I might have time later. If you're self-instructing, where are these questions coming from?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2008
    Posts
    19
    A study guide, from my math tutor, I have a teacher but he is incomprehensible! I will appreciate any help I can get I have a test on Thursday night and my anxiety level is way too high, because all the problems I am having with this study guide.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by Bananna View Post
    Find the laplace transformation of the following:
    I don't even know where to start< please Help>
    Again I will only give hints:

    You better do this using the definition of Laplace Transform.

    To do it using properties you need three things

    1) L[e^{-3t}] = \delta(t - 3)

    2) L[\int_{0}^{t} y(\tau) d\tau] = \frac{L[y(t)]}{s}

    3) Trickiest one L[\frac{\sin 2t} {t}]. This is the sinc function.Trying this separately is a good idea
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Isomorphism View Post
    Again I will only give hints:

    You better do this using the definition of Laplace Transform.

    To do it using properties you need three things

    1) L[e^{-3t}] = \delta(t - 3)

    2) L[\int_{0}^{t} y(\tau) d\tau] = \frac{L[y(t)]}{s}

    3) Trickiest one L[\frac{\sin 2t} {t}]. This is the sinc function.Trying this separately is a good idea
    Isomorphism has given some good hints. I'll give some different ones:

    1. LT \left[ e^{at} f(t) \right] = F(s - a) where F(s) = LT[f(t)]. This is one of the famous shift theorems.

    In your problem, a = -3 and f(t) = \int_0^t \frac{\sin (2\tau)}{\tau} \, d \tau.


    2. Same as Isomorphism's hint. In your problem y(t) = \frac{\sin (2t)}{t}.


    3. LT\left[ \frac{g(t)}{t} \right] = \int_{s}^{\infty} G(\tau) \, d \tau where G(s) = LT[g(t)]. In your problem g(t) = \sin(2t).


    4. LT[\sin (2t)] = \frac{2}{s^2 + 2^2}.


    5. Therefore LT\left[ \frac{\sin (2t)}{t}\right] = \int_{s}^{\infty} \frac{2}{\tau^2 + 2^2} \, d \tau = .....


    I will point out that all of these results should be known to you. I can't help wondering if the learning curve of your self-study is too steep. Have you gone through - thoroughly - the basics?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Isomorphism View Post
    [snip]

    3) Trickiest one L[\frac{\sin 2t} {t}]. This is the sinc function.Trying this separately is a good idea
    Unfortunately, it's not the sinc function. It's actually 2 sinc(t) cos(t) ...... It's best handled using the result I give in hint 3.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by mr fantastic View Post
    Unfortunately, it's not the sinc function. It's actually 2 sinc(t) cos(t) ...... It's best handled using the result I give in hint 3.
    I was not explicit since it was a hint:
    L[\frac{\sin 2t}{t}] = 2L[\text{sinc}(2t)]
    Either a change of variable when solving by basics OR the time compression property would have finished the job
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Isomorphism View Post
    I was not explicit since it was a hint:
    L[\frac{\sin 2t}{t}] = 2L[\text{sinc}(2t)]
    Either a change of variable when solving by basics OR the time compression property would have finished the job
    Yes, I thought of 2 sinc(2x) later

    But, I think getting it's transform from basics would be difficult for this member. And I don't think the transform of sinc (x) would be on the tables this member is using, which would make the time compression property unusable. Using the appropriate operational theorem is the most expeditious approach, I think.

    What would be interesting is to see what tables this member will be using in the exam ......

    By the way, please don't take this reply as a criticism of your suggestions.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. whats the laplase transformation of this one..
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: August 17th 2009, 01:53 PM
  2. Replies: 2
    Last Post: September 28th 2008, 02:26 PM
  3. Laplace Transformations, save me...
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 29th 2008, 11:10 PM
  4. Laplase Transformations! PLEASE HELP!!
    Posted in the Calculus Forum
    Replies: 8
    Last Post: April 29th 2008, 10:52 PM

Search Tags


/mathhelpforum @mathhelpforum