Recent content by joseph_18_18

Would e-s become f(t-1)H(t-1)...

I multiplied out the first brackets to get: (3-λ)(5-5λ-λ2)+(-3) + λ = 15-15λ-3λ2-5λ+5λ2+λ3-3+λ = λ3+2λ2-19λ-12... Thanks

Would the laplace of sin(t-1) be 12/s2+12 .. ? This does not appear in the table so its probably wrong.. thanks

I have been using the laplace transform table on wikipedia. How would I go about shifting it in the time domain? Have I managed to get the rest of it right? I will be back on tomorrow to try and finish the question. Thanks a lot for the help tonight :smile:

Yes that is true... the s should dissapear. The laplace of f(t-a) is e-st/s ... I think.. I tried inversing it by splitting it up and got: x = -2sint + H(t-1)sint + (?)sint.. I'm not sure what the inverse of e-s is (the ?) without the s underneath it.. Thanks.

multiplying out gave me λ3 + 2λ2 -19λ -12 which factorised (using grouping) to: (λ+2)(λ2-19) Am I doing it right? Thanks again.

The laplace of sin(at) is a/a2+s2 and cos(at) is s/a2+s2 Does this mean the e-s/(s2+12) becomes sint*e-s? If I wrote the function out as being \overline{x}2 = (-2/s)*(1/s2+1) + (e-s/s)*(1/s2+1) + (e-s)*(1/s2+1) would that make it easier to solve? Thanks

I would do this for: \overline{x} = a/(s+b) x = ae-bt and for \overline{x} = e-as/bs x = 1/b(H(t-a) and for \overline{x} = e-as/(s+b) x = e-b(t-a)H(t-a) But I'm not sure how I would find the inverse of a function with more than just a basic (s+a), etc, on the bottom... Thanks

Does this mean I have the correct roots? If so, how should I approach the eigenvectors with a repeated root? Thanks Mark

okay.. I've solved through to find: \overline{x}2(s2 +1) = -2/s + e-s/s - e-s which gives \overline{x}2 = -2/s(s-i)(s+i) = e-s/s(s-i)(s+i) + e-s/(s-i)(s+i) How would I do the partial fractions with imaginary numbers? Thanks

I was accidently using the laplace for the second derivative, not very smart of me lol.. I got the new laplace transforms: (with the boundary conditions applied) s\overline{x}1 - 1 = \overline{x}2 + 2/s - e-s/s and s\overline{x}2 = -\overline{x}1 + 1/s - e-s/s I modified the first...

Hello, this is the same person as the account jamie_18 which is getting deleted, I forgot password so had to create a new account lol... Anyways, I did the laplace for the two functions and got to s2\overline{x}1 - sx1(0) - \dot{x}1(0) = \overline{x}2 + 2/s - e-s/s and...

Yeah, sorry they were meant to have primes on them, my bad. Okay, from (3-λ -1 0) (-1 2-λ -1) (0 -1 3-λ) I did Column 1 - C3 to get (3-λ -1 0) (0 2-λ -1) (-(3-λ) -1 3-λ) I then took out (3-λ) as it's a common factor of C1 to get: (This is the step...

Homework Statement Use eigenvalues and eigenvectors to find the general solution of the system of ODEs.. x1 = 3x1 - x2 x2 = -x1 + 2x2 - x3 x3 = -x2 + 3x3 Homework Equations The Attempt at a Solution I converted that into the matrix...