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

Question

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.

anonymous · Answer

Oh, I missed x(0)=x'(0)=0. Sorry

experimentx · Answer

$$ x'' + 4l x = u(t) - u(t - \pi) $$

experimentx · Answer

u is step function.

experimentx · Answer

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 · Answer

looks like i added extra l

anonymous · Answer

why is it that it is $$1-e^{-s\pi}$$ rather than $$\frac{1-e^{-s\pi}}{s}$$

experimentx · Answer

looks like mistake from my part
anyway your job is to find the inverse of the transform.

anonymous · Answer

Alright give me a moment and I'll see if I can get the correct answer.

experimentx · Answer

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 · Answer

Thanks, I got it by using a table.