GATE 2024 AE – Question 62
For a general aviation airplane, one of the complex conjugate pair of eigenvalues for longitudinal dynamics is given by $-0.039 \pm 0.0567\,i$ (in SI units). If the system is disturbed to excite only this mode, the time taken for the amplitude of response to become half in magnitude is _______ s (rounded off to 1 decimal place).
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Correct answer: 17.71 to 17.89
Explanation
The mode behaves as $e^{-0.039t}\cos(0.0567t + \phi)$, so the amplitude decays as $e^{-0.039t}$. It falls to half when $t_{1/2} = \frac{\ln 2}{0.039} = 17.8$ s.