Advertisement
If you have a new account but are having problems posting or verifying your account, please email us on hello@boards.ie for help. Thanks :)
Hello all! Please ensure that you are posting a new thread or question in the appropriate forum. The Feedback forum is overwhelmed with questions that are having to be moved elsewhere. If you need help to verify your account contact hello@boards.ie
Hi there,
There is an issue with role permissions that is being worked on at the moment.
If you are having trouble with access or permissions on regional forums please post here to get access: https://www.boards.ie/discussion/2058365403/you-do-not-have-permission-for-that#latest

Laplace transform

  • 24-10-2012 8:16pm
    #1
    Daniel S
    Registered Users, Registered Users 2 Posts: 3,533 ✭✭✭


    Hey,

    As always, leaving cramming to the last minute, mid-term tomorrow. :o

    We are given this formula along with a Laplace transforms table:

    f(t-a)U_a(t) = (e^-as) F(s)

    The question I'm stuck on is:

    subpodimage.jsp?podtitle=Input&cdtf=MSP42381a3f6bbca03d183700005104gehbbf171g3c&i=f(t)%3Dsin(2t-6)U_3(t)&theme=1&plottype=Default&incframe=false&inctitle=false&incinput=false&mck=&spidx=1&s=38&id=MSP42371a3f6bbca03d183700001fd9664815i29i94&podidentifier=Input&subtitle=&&&view=preview&zoom=s&subselection=undefined&as=null&au=null&at=null&

    The answer is supposed to be:

    subpodimage.jsp?podtitle=Input&cdtf=MSP11561a3f6e4eaa8head1000037agd5c9238b44g1&i=%3D%20(2%2F(s%5E2%20%2B%204))(e%5E-(3s))&theme=1&plottype=Default&incframe=false&inctitle=false&incinput=false&mck=&spidx=1&s=9&id=MSP11551a3f6e4eaa8head1000012h72c13hief459f&podidentifier=Input&subtitle=&&&view=preview&zoom=s&subselection=undefined&as=null&au=null&at=null&


Comments

  • #2
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,852 Mod ✭✭✭✭Michael Collins


    Can you express [latex] f(t)=\sin(2t-6) [/latex] as a different function of the form: f(t-3)

    For example the function of x, f(x)=3x-6, can be re-written as a function of x-2, f(x-2)= 3(x-2).

    If you can do this, then all that's left to do is to apply the formula you gave above from the table of Laplace transform properties


  • #3
    Daniel S
    Registered Users, Registered Users 2 Posts: 3,533 ✭✭✭Daniel S


    Michael Collins wrote: »
    Can you express [latex] f(t)=\sin(2t-6) [/latex] as a different function of the form: f(t-3)

    For example the function of x, f(x)=3x-6, can be re-written as a function of x-2, f(x-2)= 3(x-2).

    If you can do this, then all that's left to do is to apply the formula you gave above from the table of Laplace transform properties

    What do I do with the sin and the 2? Do I just ignore them or? :o


  • #4
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,852 Mod ✭✭✭✭Michael Collins


    No sorry, I was just giving an example of how you can rewrite a function. It all comes down to that transform you gave:

    [latex] f(t-a) u_{a}(t) \to e^{-as} F(s) [/latex]

    Can you figure out what "a" should be?


  • #5
    Daniel S
    Registered Users, Registered Users 2 Posts: 3,533 ✭✭✭Daniel S


    I can get the answers out now. :D (The important bit :pac: )

    But some questions have U1/2/3 which I don't understand? What does that do? It doesn't seem to affect the answer.

    EDIT: Just got it now... :o


  • #6
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,852 Mod ✭✭✭✭Michael Collins


    Daniel S wrote: »
    I can get the answers out now. :D (The important bit :pac: )

    But some questions have U1/2/3 which I don't understand? What does that do? It doesn't seem to affect the answer.

    EDIT: Just got it now... :o

    Well for anyone else that comes across this: u(t) is the unit step function, and it is just there to ensure that when a signal is time-shifted to the right by "a" (equivalent to multiplying by e^{-as} in the Laplace domain), that the shifted version remains zero for t<a, since f(t)=0 for t<0 before shifting (this is always* assumed).

    *Unless you're working with the bilateral Laplace transform, which I've never seen in any 3rd level course!


  • Advertisement
Advertisement