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January 14th, 2012, 06:31 AM   #11
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Re: solve differential lap ace where f(t)=square wave

How is this?
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January 14th, 2012, 02:38 PM   #12
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Re: solve differential lap ace where f(t)=square wave

Still a problem...

??????
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January 15th, 2012, 01:45 AM   #13
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Re: solve differential lap ace where f(t)=square wave

yeah thought I may be going in the wrong direction there.
how is this for a strong sprint to the finish?
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January 15th, 2012, 07:44 AM   #14
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Re: solve differential lap ace where f(t)=square wave

Quote:
Originally Posted by defunktlemon
yeah thought I may be going in the wrong direction there.
how is this for a strong sprint to the finish?
Completely wrong. A mix of s and t in one equation is not good.
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January 16th, 2012, 03:08 PM   #15
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Re: solve differential lap ace where f(t)=square wave

any hints please - I'm not seeing this
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January 17th, 2012, 08:50 AM   #16
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Re: solve differential lap ace where f(t)=square wave

use the shifting property

http://www.intmath.com/laplace-trans...properties.php
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January 24th, 2012, 04:26 PM   #17
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Re: solve differential laplace where f(t)=square wave

Ok, seeing you're getting lots of errors along the solution, I'll try to go step by step, as clearly as possible.



where for , otherwise.

Then we can represent by the Heaviside function like this:



Thus we have



We use the Laplce transform, setting for an easier working.

Using the rules of tranforms of derivatives and the transform of the Heaviside function, we get the following equation:



Recalling y(0) = y'(0) = 0 we get



Factor out



Note that and write



Use partial fractions:



Multiply the last expression through to get



Use the theorems and to obtain . Remeber that . You get



You can group in terms of the Heaviside function to get



So it is neater to read. You can see you actually have a function that is being shifted:





So you actually have:



Rings a bell? If you're up to it, check that indeed you have

y''-3y'+2y = S(t)

(You can use GeoGebra, setting as the heaviside function, ,, and then . Input then , and check what you get.)
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