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Lecture 11

AER 403 Lecture Notes - Lecture 11: Damping Ratio, Vibration, Inverse Trigonometric FunctionsPremium

4 pages68 viewsWinter 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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