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

MATH152 April 2022
Other MATH152 Exams

### Question B5 (c)

With the variables ordered ${\textstyle I,V_{1},V_{2}}$, let the matrix of the system of differential equations be ${\textstyle A}$. (You don’t need to find ${\textstyle A}$.) 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 ${\textstyle I(t)}$, ${\textstyle V_{1}(t)}$, ${\textstyle V_{2}(t)}$ that is not oscillating and not zero. Note: you don’t need the results from (a) and (b) to attempt (c).

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