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January 14th, 2012, 06:31 AM  #11 
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
How is this?

January 14th, 2012, 02:38 PM  #12 
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  Re: solve differential lap ace where f(t)=square wave
Still a problem... ?????? 
January 15th, 2012, 01:45 AM  #13 
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
yeah thought I may be going in the wrong direction there. how is this for a strong sprint to the finish? 
January 15th, 2012, 07:44 AM  #14  
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  Re: solve differential lap ace where f(t)=square wave Quote:
 
January 16th, 2012, 03:08 PM  #15 
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
any hints please  I'm not seeing this

January 17th, 2012, 08:50 AM  #16 
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  Re: solve differential lap ace where f(t)=square wave 
January 24th, 2012, 04:26 PM  #17 
Senior Member Joined: Dec 2011 From: Argentina Posts: 216 Thanks: 0  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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