Science:Math Exam Resources/Courses/MATH152/April 2022/Question B5 (c)/Statement

With the variables ordered $I, V_{1}, V_{2}$ , let the matrix of the system of differential equations be $A$ . (You don’t need to find $A$ .) Consider the following Matlab result:

> [P,D] = eig(A) 

P = 
    0.5 - 0.34i     0.5 + 0.34i     0.22 + 0.00i
    0.62 + 0.00i    0.62-0.00i      0.85 + 0.00i
    -0.43 - 0.21i   -0.43 + 0.21i   0.47 + 0.00i

D = 
Diagonal Matrix
-0.15 + 0.17i       0                   0
0                   -0.15 - 0.17i       0
0                   0                   -0.77 + 0.00i

There exist initial conditions that result in a non-oscillating solution (a real solution that does not involve sin and cos). Find one such solution $I (t)$ , $V_{1} (t)$ , $V_{2} (t)$ that is not oscillating and not zero. Note: you don’t need the results from (a) and (b) to attempt (c).