Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    How is this true? Note: L() means Laplace transform.

    L(\delta(t-2\pi)*cos(t))=e^{-2\pi s}

    I get that the exponential comes from the delta function, but why did cos(t) disappear in the Laplace transform?
    Offline

    0
    ReputationRep:
    Roughly...

    

L(\delta(t-2\pi) cos(t)) = \int_0^\infty e^{-s t} \delta(t-2\pi) cos(t) dt = e^{-s 2\pi} cos(2\pi) = e^{-2\pi s}

    Edit: I'm assuming that your asterisk represents multiplication and not convolution, in which case the result would be incorrect.

    (Original post by D-Day)
    How is this true? Note: L() means Laplace transform.

    L(\delta(t-2\pi)*cos(t))=e^{-2\pi s}

    I get that the exponential comes from the delta function, but why did cos(t) disappear in the Laplace transform?
    • Wiki Support Team
    Offline

    14
    ReputationRep:
    Wiki Support Team
    More generally, delta(t-a) f(t) = delta(t-a) f(a) everywhere.

    (Edit: strictly, this isn't a meaningful statement; clearly both are 0 everywhere away from a, and at t = a both are undefined. This post is colloquial for "their integrals are equal over any interval".)
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: August 6, 2009

University open days

  1. Loughborough University
    General Open Day Undergraduate
    Fri, 21 Sep '18
  2. University of Cambridge
    Churchill College Undergraduate
    Fri, 21 Sep '18
  3. Richmond, The American International University in London
    Undergraduate Open Day Undergraduate
    Fri, 21 Sep '18
Poll
Which accompaniment is best?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.