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January 7th, 2012, 06:34 AM  #1 
Member Joined: Dec 2011 From: Oxford, UK Posts: 48 Thanks: 0 Math Focus: Linear Algebra / 3d Math / Geometry & Trig / Topology  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 
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(t1)  u(t2) 
January 8th, 2012, 04:02 AM  #3 
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
like this?

January 8th, 2012, 04:05 AM  #4 
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
sorry  i mean like this?

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(t1)  u(t2)

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(t1)u(t2) 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 Now calculate Laplace transform of both sides. 
January 9th, 2012, 04:02 PM  #8 
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 9th, 2012, 04:03 PM  #9 
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
sorry kinda wrong image how is this? 
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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