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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 where m = 2 , m k = 2 . Case I: 2 2-The 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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