GATE 2014 EC (EC3) – Question 31
Input $-3e^{2t}u(t)$, with unit step u(t), drives a system with transfer $(s-2)/(s+3)$. Output initial value is −2. Find steady-state output.
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Correct answer: -0.01 to 0.01
Explanation
The transfer relation corresponds, for t>0, to y′+3y=u′−2u. With u=−3e²ᵗ, the right side is−6e²ᵗ+6e²ᵗ=0. The supplied initial value gives y(t)=−2e⁻³ᵗ, which decays to **0**. The growing exponential is cancelled by the system zero at s=2; directly applying the final-value theorem without checking poles would be unsafe.