CE 573: Structural Dynamics HW#3 Supplemental Problem Ry (x)xkcgmv = constantFrameCenter of Masshy(t)Y(t)WheelyoGiven: A car can be (crudely) modeled as a single degree of freedom system having the entire car’s mass mlumped at the center of mass and connected to the frame (modeled as a rigid bar) by a linear spring (stiffness = k, unstretched length = lo) and a linear damper (damping constant = c). The frame, in turn, is a fixed height habove the wheel, which rides over a rough road whose vertical height above the fixed x-axis is given by a known function yR(x). The car starts at the location x=0at the initial time t=0(assume that yR(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 yobe 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
This is the end of the preview.
access the rest of the document.