MAE 488 - Quiz 6 Exam 2026 Questions
and Answers
Common input (test) signals - Correct answer-Impulse, Step, ramp, parabolic,
sinusoid, and square wave
Free Response - Correct answer-due to the initial condition 𝑥(𝑡) = 𝑥(0)𝑒^(−𝑎)
Forced Response - Correct answer-due to the forcing function 𝑥(𝑡) = 𝑏/𝑎 (1 −
𝑒^(−𝑎))
Steady State Reponse - Correct answer-remains with time 𝑥(𝑡) = 𝑏/𝑎
Transient Response - Correct answer-that disappears (decays to zero) with time
𝑥(𝑡) = (𝑥(0) − 𝑏/𝑎) 𝑒^(−𝑎)
characteristic equation of 2nd order system - Correct answer-𝑚𝑠^2 + 𝑐𝑠 + 𝑘 = 0
damped natural frequency - Correct answer-𝜔_𝑑 = SQRT(𝑘/𝑚 − (𝑐/2𝑚)^2)
natural frequency - Correct answer-𝜔_n = SQRT(𝑘/𝑚)
critical damping value. - Correct answer-𝑐 = 2*SQRT(𝑚k)
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and Answers
Common input (test) signals - Correct answer-Impulse, Step, ramp, parabolic,
sinusoid, and square wave
Free Response - Correct answer-due to the initial condition 𝑥(𝑡) = 𝑥(0)𝑒^(−𝑎)
Forced Response - Correct answer-due to the forcing function 𝑥(𝑡) = 𝑏/𝑎 (1 −
𝑒^(−𝑎))
Steady State Reponse - Correct answer-remains with time 𝑥(𝑡) = 𝑏/𝑎
Transient Response - Correct answer-that disappears (decays to zero) with time
𝑥(𝑡) = (𝑥(0) − 𝑏/𝑎) 𝑒^(−𝑎)
characteristic equation of 2nd order system - Correct answer-𝑚𝑠^2 + 𝑐𝑠 + 𝑘 = 0
damped natural frequency - Correct answer-𝜔_𝑑 = SQRT(𝑘/𝑚 − (𝑐/2𝑚)^2)
natural frequency - Correct answer-𝜔_n = SQRT(𝑘/𝑚)
critical damping value. - Correct answer-𝑐 = 2*SQRT(𝑚k)
©COPYRIGHT 2025, ALL RIGHTS RESERVED 1
