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January 7th, 2012, 06:34 AM   #1
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solve differential laplace where f(t)=square wave

Hi: I have the following problem. I am trying to solve the attached image but not sure how to represent the square wave as a function.
f(t)=1 where t>1 and t<2 or something like that?
thanks
Attached Images
 Screen Shot 2012-01-07 at 15.35.40.png (10.3 KB, 649 views)

 January 7th, 2012, 09:51 AM #2 Senior Member   Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0 Re: solve differential lap ace where f(t)=square wave you can represent it using the unit step function (Heaviside Function) u(t). f(t) = u(t-1) - u(t-2)
January 8th, 2012, 04:02 AM   #3
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Re: solve differential lap ace where f(t)=square wave

like this?
Attached Images
 Screen Shot 2012-01-08 at 13.02.18.png (18.1 KB, 626 views)

January 8th, 2012, 04:05 AM   #4
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Re: solve differential lap ace where f(t)=square wave

sorry - i mean like this?
Attached Images
 Screen Shot 2012-01-08 at 13.09.12.png (18.1 KB, 626 views)

 January 8th, 2012, 02:50 PM #5 Senior Member   Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0 Re: solve differential lap ace where f(t)=square wave no, replace f(t) by f(t) = u(t-1) - u(t-2)
 January 9th, 2012, 01:34 PM #6 Member   Joined: Dec 2011 From: Oxford, UK Posts: 48 Thanks: 0 Math Focus: Linear Algebra / 3d Math / Geometry & Trig / Topology Re: solve differential lap ace where f(t)=square wave so I get: y''=u(t-1)-u(t-2) What is it i'm doing here?
 January 9th, 2012, 01:56 PM #7 Senior Member   Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0 Re: solve differential lap ace where f(t)=square wave No, you get $y''-3y'+2y=u(t-1) - u(t-2)$ Now calculate Laplace transform of both sides.
January 9th, 2012, 04:02 PM   #8
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Re: solve differential lap ace where f(t)=square wave

How is this?
Attached Images
 Screen Shot 2012-01-09 at 23.22.40.png (32.9 KB, 606 views)

January 9th, 2012, 04:03 PM   #9
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Re: solve differential lap ace where f(t)=square wave

sorry -kinda wrong image
how is this?
Attached Images
 Screen Shot 2012-01-10 at 01.07.07.png (31.6 KB, 606 views)

 January 10th, 2012, 03:20 AM #10 Senior Member   Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0 Re: solve differential lap ace where f(t)=square wave fourth from the last last it shoud be ...-3sy'...

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