The Attempt at a Solution
Using basic physics knowledge I got
Sub in values and use laplace transforms and rearrange partial fraction and I found that
By doing this I am assuming that the xII and xIII will equal 0 when t=0 because this is not stated at all in the question. do you believe this is correct?
Finding the initial displacements by subbing in t=0 for both x_1 and x_2 comes out with what is written in the question 1 and 2, respectively.
However, when I try to sub t=0 into the differentials of the 2 above equations. I believe I should receive the initial velocities stated in the question. however I do not receive these results.
I receive 4/3 for x1 and -2/3 for x2
the difference between these values and the actual values appears to differ once I differentiate the sin2t and it is multiplied by 2
Does anyone know if I should receive the values listed in the question using this methods and have just made a calculation error in my working earlier on, or should I have done something differently.
Also, the next part of the questions asks to use a matrix and eigenvalues/eigenvectors to solve it. any pointers to help me get started
Thanks very much