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HW3supp - CE 573 Structural Dynamics HW#3 Supplemental...

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CE 573: Structural Dynamics HW#3 Supplemental Problem R y (x) x k c g m v = constant Frame Center of Mass h y(t) Y(t) Wheel y o Given : A car can be (crudely) modeled as a single degree of freedom system having the entire car’s mass m lumped at the center of mass and connected to the frame (modeled as a rigid bar) by a linear spring (stiffness = k , unstretched length = l o ) and a linear damper (damping constant = c ). The frame, in turn, is a fixed height h above the wheel, which rides over a rough road whose vertical height above the fixed x -axis is given by a known function y R (x) . The car starts at the location x=0 at the initial time t=0 (assume that y R (x=0) = 0) and it moves to the right with a constant horizontal speed v . Let Y(t) be the height of the center of mass above the fixed x -axis, let y o be the static equilibrium height of the center of mass at time t=0 , and let y(t) be the height of the center of mass above this static equilibrium position. Gravity acts downward as shown. Required : (a) Determine the equation of motion for the car’s center of mass in terms of
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