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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
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File Type: png Screen Shot 2012-01-07 at 15.35.40.png (10.3 KB, 649 views)
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January 7th, 2012, 09:51 AM   #2
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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)
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January 8th, 2012, 04:02 AM   #3
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Re: solve differential lap ace where f(t)=square wave

like this?
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File Type: png Screen Shot 2012-01-08 at 13.02.18.png (18.1 KB, 626 views)
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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?
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File Type: png Screen Shot 2012-01-08 at 13.09.12.png (18.1 KB, 626 views)
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January 8th, 2012, 02:50 PM   #5
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Re: solve differential lap ace where f(t)=square wave

no, replace f(t) by f(t) = u(t-1) - u(t-2)
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January 9th, 2012, 01:34 PM   #6
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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?
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January 9th, 2012, 01:56 PM   #7
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Re: solve differential lap ace where f(t)=square wave

No, you get



Now calculate Laplace transform of both sides.
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January 9th, 2012, 04:02 PM   #8
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Re: solve differential lap ace where f(t)=square wave

How is this?
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File Type: png Screen Shot 2012-01-09 at 23.22.40.png (32.9 KB, 606 views)
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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?
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January 10th, 2012, 03:20 AM   #10
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Re: solve differential lap ace where f(t)=square wave

fourth from the last last it shoud be ...-3sy'...
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