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ase330m-fall08-hw02 - ASE330MFall2008:Homework#2...

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ASE 330M Fall 2008: Homework #2 Due Monday, September 29 th The diagram below illustrates a particle P of mass m that is constrained to move radially along a recessed channel on a spinning turntable. The motion of the mass is subject to some stiffness and frictional losses, each represented by a linear spring of constant k and a linear damper of constant c, respectively. The unstretched length of the linear spring is roughly 0.10 m. In the diagram, the unit vectors ˆ i u are fixed on the spinning turntable so that 1 ˆ u is aligned with the channel, 3 ˆ u is normal to the plane of motion, and 2 3 1 ˆ ˆ ˆ u u u . An inertial coordinate system is defined through unit vectors ˆ i e . The relative orientation of the turntable with respect to the inertial frame is given by the angle   t such that when   0 t , the ˆ i u and ˆ i e unit vectors are aligned. The orientation illustrated below is a top view of the turntable such that gravity acts into the page (i.e. down).
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  • Spring '10
  • Trigraph, Equilibrium point, linear state space, Unit  Vectors, constant parameter.  Derive, linear  spring

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