ENME361 Quiz 3 Solution

ENME361 Quiz 3 Solution - B Balachandran ENME 361...

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B. Balachandran ENME 361 Vibrations Fall 2008 Solution to Quiz #3 (September 18, 2008; Duration: ten minutes) 1a) For the system shown to the right, obtain an expression for the position vector of the mass m with respect to the point O . 1b) By using the result from 1a), determine an expression for the velocity vector of the mass m in terms of the unit vectors 1 e and 2 e . Some useful relations are the following: 12 ,, dd dt dt θ == ×= × ± e' e' k ω e' ω e' ω m ϕ J O R r e 1 e 2 Pivot O O e 2 e 1 ± Position vector: () 11 112 cos sin cos sin m Rr r r = + ′′ =+ + + re e eee ee Velocity vector: cos cos sin sin m m d r r dt dt dt dt dt ϕϕ + + + + + e Ve e Since 2 2 2 1 and dt dt θθ = = ±± ± ± ω ek ω e e , we have ( ) 2 1 sin cos cos sin sin cos m rR r r r r ϕθ =− + + + + + + + ± e e e 2) What is an inertial reference frame?
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This note was uploaded on 02/13/2011 for the course ENME 361 taught by Professor Yoo during the Spring '11 term at Maryland.

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