Question

1- One engineer is studying a specific mathematical modeling for one of his projects and came up with the following system of differential equations: y' = -10a + 81. But the system above does not produce an oscillatory behavior as he expected. (a) Solve the system (1) to make sure the engineer did not make any mistake (b) After realizing the system did not produce the desired output, he decided to study the effect of one of its components and proposed to himself the following change where e is a real number. He wants to check if a perturbation in one of the parameters will produce the desired output. He asked for help for the Math 2240 students. For which value of ε the system would produce an oscillatory behavior with frequency 100 Hz? (Hint: This is the condition on the imaginary part of the complex eigenvalues of the coefficient matrix.)

Answer 1

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LA-gives -tve for L 2. -1 D 2. 15-1115 15-.NIS. So sgen ve (for ン. 2 2.0 2- 2 2.o

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