Differential Equations
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Last updated 7:51 PM on 4/8/25
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14 Terms
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Undamped Free Motion
mx'' + kx = 0
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Damped Free Motion
mx'' + cx' + kx = 0
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overdamped
distinct real roots
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Critically damped
repeated real roots
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underdamped
complex conjugate roots
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Undamped Forced Motion
mx'' + kx = F(t)
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Damped Forced Motion
mx'' + kx + cx' = F(t)
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critically damped
c²=4mk
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underdamped
c²<4mk
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overdamped
c²>4mk
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amplitude
C=sqrt(c1²+c2²)
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period
2π/w
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alpha
arctan(c2/c1)
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Vibrations
Ccos(wt-alpha)
Note 
Flashcards (179)