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MAE 488 Exam 2 (with Quizzes 4-7) well answered to pass
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MAE 488 Exam 2 (with Quizzes 4-7) well answered to pass
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MAE 488 Exam 2 (with Quizzes 4-7)What happens to the free response of a system when it's stable poles (roots of the characteristic
equation) are moved to the left on the complex plane? - correct answer ✔✔It decays faster
What happens to the free response of a system when it's stable poles (roots of the characteristic
equation) are moved downward (i.e. towards the real axis) on the complex plane? - correct answer
✔✔The frequency decreases
What type of free response will a system have if it has poles on the jw axis? - correct answer
✔✔Oscillatory
(T/F) The magnitude of the response of a system at resonance depends on the damping ratio ζ. - correct
answer ✔✔True
Label these response types from L to R, top to bottom:
x(t) = x0*e^(-at) + b/a*(1 - e^(-at))
x(t) = b/a + (x0 - b/a)*e^(-at) - correct answer ✔✔free, forced, steady-state, transient
The _______________ is the part of the response that is due to the initial condition. If the initial
conditions are zero, there is no free response. - correct answer ✔✔free response or initial condition
response
The ___________________is the part of response due to the forcing function (i.e. input). If the input is
zero, there is no forced response. - correct answer ✔✔forced response
The ____________________ is the part of the response that remains with time - correct answer
✔✔steady-state response
The _______________ is the part of the response that disappears (decays to zero) with time. - correct
answer ✔✔transient response
, The characteristic equation of a 2nd order response is: - correct answer ✔✔ms^2 + cs + k = 0
The roots of the characteristic equation of a 2nd order response are: - correct answer ✔✔a +/- jb, where
a = -c/2m and b = sqrt(k/m - (c/2m)^2) = wd
The damping coefficient is represented by the letter _________ , which reduces the frequency of
oscillation from the __________ - correct answer ✔✔c; natural frequency
____________ is the natural frequency - correct answer ✔✔wn
If c = 0, the system doesn't have any damping and is equivalent to a _____________ - correct answer
✔✔mass-spring system
_____________ is the damped frequency - correct answer ✔✔wd
If wd is zero or imaginary, the system will NOT _________ - correct answer ✔✔oscillate, and the roots
will be real and equal
The value of c for which wd will be zero is ________. This is known as the __________ value - correct
answer ✔✔c = 2*sqrt(mk); critical damping value
An oscillatory response has _________ roots, while a non-oscillatory response has _______ roots. -
correct answer ✔✔complex conjugate; real
ζ = c/(2*sqrt(mk)) is known as the _________ - correct answer ✔✔damping ratio/factor, or the ratio of c
to the critical damping value.
The standard form is _______________ - correct answer ✔✔Y(s) = wn^2/(s^2 + 2ζwn*s + wn^2) (laplace
table #21)
wd = _________ - correct answer ✔✔wn*sqrt(1 - ζ^2)
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