Question

Laplace help?

Answer 1

This ones got me frustrated. I think that I may have worked it out all right but am unsure. Will someone check over it for me?

Answer 2

and wolfram alpha disagrees with my answer http://www.wolframalpha.com/input/?i=y%27%27%2B4y%3Dpiecewise [{{t%2C0%3C%3Dt%3C1}%2C{0%2C1%3C%3Dt}}]%2C+y%280%29%3D0%2C+y%27%280%29%3D0

Answer 3

how to you do laplace transform of box function??

Answer 4

Not sure what you mean, this is all new to me

Answer 5

i'm step behind you ..
http://openstudy.com/study#/updates/4fd32a70e4b057e7d2220d1d

Answer 6

if i solve it now ... i'll be doing laplace transfrom in few hours
g(x) = u(t) - u(t-1) is a box function <--- haven't done it's laplace transfrom yet

Answer 7

This is the table that I use, http://tutorial.math.lamar.edu/pdf/Laplace_Table.pdf , it has transforms for the unit step function

Answer 8

I think i get an idea ... just an idea though
\[ \int_0^\infty e^{-st}(u(t)-u(t-1))ds = \int_0^1e^{-st}dt \]

Answer 9

Thanks .. there you have it ..no 27

Answer 10

that would be
\[ \frac{1 - e^{-s}} s\]

Answer 11

So we have RHS!! let's see what is LHS

Answer 12

\[ s^2 F(s) - sy(0) - s^2y'(0) + 4(sF(s) - y(0)) = \frac{1 - e^{-s}}s \\
F(s)(s^2+4s) = \frac{1 - e^{-s}}s \]

Answer 13

I'm getting something stupid
http://www.wolframalpha.com/input/?i=inverse+Laplace+transform+%281-e^-s%29%2F%28s%28s^2%2B4s%29%29

Answer 14

Oh sorry, i didn't realize it was t, i saw it like 1
\[ \text {the box function is : }t(u(t) - u(t-1))\]
Laplace transfrom of this is
\[ \frac{1 - e^{-s}}{s^2}\]

Answer 15

the y should be
http://www.wolframalpha.com/input/?i=inverse+Laplace+transform+%281-e^-s%29%2F%28s^2%28s^2%2B4s%29%29

Answer 16

looks like i made another mistake again
y looked like y'
LHS must be
\[ F(s)(s^2+4)\]
The answer must be
http://www.wolframalpha.com/input/?i=inverse+Laplace+transform+%281-e^-s%29%2F%28s^2%28s^2%2B4%29%29

which is harmonic

Answer 17

what a weird result !-_-!

Answer 18

This is good exam revision for me so I thought I give it a shot and I got the same as you.
Heres my working if your interested