anonymous
  • anonymous
A mass-spring-dashpot system with external forcing function: mx''+cx'+kx=f(t) m=1; k=4l c=0; f(t) = 1 when 0 <= t < pi; f(t) = 0 when t >= pi I get: s^2X(t) + 4X(t) = F(t) F(t) = (1-e^(-pi s))/(s^3) But that seems to be wrong.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Oh, I missed x(0)=x'(0)=0. Sorry
experimentX
  • experimentX
\[ x'' + 4l x = u(t) - u(t - \pi) \]
experimentX
  • experimentX
u is step function.

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experimentX
  • experimentX
Looking at Transform table, \[ s^2 F(s) + 4l F(s) = 1 - e^{-s \pi } \\ F(s) = \frac{1 - e^{-s\pi }}{4l + s^2 }\] Find the inverse transform.
experimentX
  • experimentX
looks like i added extra l
anonymous
  • anonymous
why is it that it is \[1-e^{-s\pi}\] rather than \[\frac{1-e^{-s\pi}}{s}\]
experimentX
  • experimentX
looks like mistake from my part anyway your job is to find the inverse of the transform.
anonymous
  • anonymous
Alright give me a moment and I'll see if I can get the correct answer.
experimentX
  • experimentX
http://www.wolframalpha.com/input/?i=Inverse+Laplace+Transform+%28+1+-+e%5E%28-s+Pi%29%29%2F%28s%28s%5E2+%2B+4%29%29 make partial decomposition ... use convolution if necessary.
anonymous
  • anonymous
Thanks, I got it by using a table.

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