Recent content by jake96

thanks for your help everyone, I've managed to get the correct answer using a 2x2 matrix made from the original equations

OK, so I believe I have gotten my four y equation out with 4 unknowns c1, c2, c3 and c4. What will these 4 equations equal so that I am able to determine the value of each 'c'

also I just want to double check, if I had the eigenvalue of 'i' and the corresponding eigenvector (-i,1,-i,1) the first term of the first y equation would be -i(acost+ibsint) with a and b as unknowns and so on with each value and vector

ive only ever used it for 2x2 matrix's, I assume this way I would receive 4 equations with 4 unknowns? I'm still a little unsure as to how those unknowns are calculated, will the 4 equations be equal to the 4 y equations that Ray Vickson listed?

So now that I have my eigenvalues and eigenvectors. I believe I now use them for the exponential matrix and that should give me my sin and cos equations of x1 and x2 from earlier in the question. However I am unsure how I am able to reach this point as I have not fully learned this yet and am...

I am also having trouble finding good sites online that delve into complex eigenvalues and eigenvectors for any matrix above 2x2. My textbook does touch on this and i was just wondering if anyone knew of anywhere good that i can find some examples to refer to.

so I got the Eigen values as i, -i, 2i, -2i for i, i found an Eigen value of -i 1 -i 1 Does this seem correct? Now if i find the eigenvectors for the other eigenvalues. i can use this in the exponential equation and eventually reach values of x1 and x2 which should be the same answers from...

thanks

Would you have any pointers to help me get started on doing this problem with a matrix using eigenvalues and eigenvectors I can't seem to see where the matrix will come in for this question. I'm confident I can solve the eigenvalues and vectors once I've gotten out the matrix. Thanks again

I see my error now, I had 1 over instead of 2 over which will cause the factor to be 1/2. thanks very much

so the answers we have been talking about should be the correct ones (laplace then algebra) cos the first time I used algebra before laplace and that resulted in x''(0) and x'''(0) values which are not stated

ahhh, thankyou very much. that would fix the problem I've had with all the answers I've received because the sin2t has always been double what it should be. it appears that the method I use comes up with multiple answers that all equal the correct displacement and velocities. Is this correct...

sub those into A(s/(s2+4))+b(1/(s2+4))+C(s/(s2+1))+D(1/(s2+1)) and that dwindles down to (1/3)(s/(s2+4))-(1/(s2+4))+(5/3)(s/(s2+1)) then the inverses I mentioned above comes up with x2=(1/3)cos2t-sin2t+(5/3)cost Are these Inversions correct?

the only inversion I used was for s/(s2+a) and 1/(s2+a) which go to sin and cos

From here (2s3-s2+7s-1)/((s2+4)*(s2+1)) I used partial fraction expransions and found that 2s3-s2+7s-1=(A+C)s3+(B+D)s2+(A+4C)s+(B+4D) that gave me A+C=2, B+D=-1, A+4C=7 and B+4D=-1 therefore A=(1/3), B=-1, C=(5/3) and D=0