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Lecture 11

AER 403 Lecture 11: AER 403 W11
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4 Pages
62 Views
Winter 2015

Department
Aerospace
Course Code
AER 403
Professor
Fengfeng Xi
Lecture
11

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Damping ratio
• Notethatc=ξcC
c/m = ξcC/m = ξωn ωn = k/m/ since cC = km/ =
mk/m/ = mωn
• Now
s1,2 = -c/2m ±[(c/2m)2 k/m]1/2= [-ξ±ξ-/]ωn
• Solution is rewritten as
x e nt (Ae( Decay term
(no oscillation)
2
1/2 2 1/2
1) nt Be ( 1) nt )
three cases
(decay or oscillation)
What determines natural frequency? What determines amplitude and
phase?
26,
| 25
Under-damped Oscillatory Motion
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Description
Damping ratio Notethatc=cC c/2m = (cC/2m) = n n = (k/m)1/2 since cC = 2(km)1/2 = 2m(k/m)1/2 = 2mn Now s1,2 = -c/2m [(c/2m)2 k/m]1/2= [-(2-1)1/2]n Solution is rewritten as x e nt (Ae( Decay term (no oscillation) 2 1/2 2 1/2 1) nt Be ( 1) nt ) three cases (decay or oscillation) What determines natural frequency? What determines amplitude and phase? 26, | 25 Under-damped Oscillatory Motion
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