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PLEASE ATEMPT ALL QUESTION.

Questions

For the system described by the 2nd order differential equation below, assuming u-0,

A-5 and B-6 determine the following:

x" + Ax' + Bx = u

A) The roots of the system. Explain the response of the system and if the system

is stable/unstable?

marks

B) The natural frequency and damping factor of the system. Explain how by using

the damping factor you could predict the system response and if the system is

stable/unstable, oscillatory/non-oscillatory.

C) Using Simulink, compare both numerical and analytical solutions, sketch the

output vs time and describe the system behaviour (stability and steady state

value). Assume that: x(0)=1, x'(0)=0 which results in C₁--2 and C₂=3.

fob

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