University Physics with Modern Physics with Mastering Physics (11th Edition)

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13.98: Denote the position of a piece of the spring by 0 ; = l l is the fixed point and L l = is the moving end of the spring. Then the velocity of the point corresponding to , l denoted ( 29 L l v l u u = is , (when the spring is moving, l will be a function of time, and so u is an implicit function of time). a)
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Unformatted text preview: , dl dm L M = and so , 2 1 2 1 2 3 2 2 dl l L Mv u dm dK = = and . 6 2 2 2 3 2 Mv dl l L Mv dK K L = = = ∫ ∫ b) , or , = + = + kx ma kx mv dt dx dt dv which is Eq. ( 29 . 4 . 13 c) m is replaced by , 3 M so . and 3 3 M M k M ω = ′ =...
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