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Unformatted text preview: PHYS 3202 Classical Mechanics II  Quiz #2 Please write your name. Conceptual (circle ALL that apply  there may be one or more correct items in each problem) 1. (4 points) The Hamiltonian has the same dimension as A. the product of someones mass and height B. the product of someones weight ( mg ) and height ( h ) C. work D. action 2. (3 points) If a systems Hamiltonian is H ( q 1 ,q 2 ,p 1 ,p 2 ,t ) = p 2 1 2 m 1 + p 2 2 2 m 2 + k 2 ( q 1 q 2 ) 2 , where m 1 , m 2 , and k are positive constants, and m 1 6 = m 2 , which of the following quantities are conserved? A. q 2 B. p 1 + p 2 C. H 3. (2 points) For the Hamiltonian system H ( q,p,t ) = c p 2 c 1 q 2 + c 2 q 4 , where c , c 1 , and c 2 are positive constants, exactly how many points on the phase plane are stationary (namely satisfy q = 0 and p = 0 simultaneously)? A. 1 B. 2 C. 3 D. 4 4. (2 points) An object is described by the Hamiltonian H = p 2 2 m + V ( q ) where V ( q ) = mgq at q > 0 and V ( q ) = Kq at q < 0. Assume that m , g , and K are positive constants, and K mg (think of a pingpong ball that bounces perpetually on the ground).on the ground)....
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 Spring '11
 Tan
 mechanics, Mass

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