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Unformatted text preview: A c 1 sin = and A c 2 cos = . #8 Free Damped Motion – We will assume that the damping force is given by a constant multiple of dt dx . The motions will be modeled by 2 2 2 2 = + + x dt dx dt x d ϖ λ where m β = 2 , m k = 2 . Case I: 2 2The system is said to be overdamped . The solution is + =t e c e c e t x t t 2 2 2 2 2 1 ) ( . This equation represents a smooth an nonoscillatory motion. Case II: 2 2 =The system is said to be critically damped . The solution is ( 29 t c c e t x t 2 1 ) ( + =. Any slight decrease in the damping force would result in oscillatory motion. Case III: 2 2 <The system is said to be underdamped . The solution is ( 29 t c t c e t x t 2 2 2 2 2 1 sin cos ) (+=. #22...
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 Fall '10
 PamelaSatterfield
 Differential Equations, Equations, Simple Harmonic Motion, equilibrium position, free undamped motion

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