GATE 2020 IN – Question 60
A state model is $\dot x_1=x_2$, $\dot x_2=-6x_1-5x_2$, with $x_1(0)=0,x_2(0)=1$. Find x₂(1), to two decimal places.
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Correct answer: -0.13 to -0.11
Explanation
Eliminate x₂ to get $x_1\prime\prime+5x_1\prime+6x_1=0$, with roots −2 and −3. Initial conditions give $x_1=e^{-2t}-e^{-3t}$, so $x_2=-2e^{-2t}+3e^{-3t}$. At t = 1 this is $-2e^{-2}+3e^{-3}=-0.12131$, rounding to −0.12.
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