ME 143 1st Long Exam (Make up exam - Nocomora)

For the figure on the left above, set up the differential equation of motion, give the solution and graph the motion of the mass m1, if the initial conditions dictate that the mass starts with zero velocity. By equations show the per cent change in the period if m2 is twice m1

For the system shown on the left, the total mass of the block is meq, and the block is connected to a damper with damping constant of ceq and spring constant of keq. Within the block a rotor has an imbalance m with an eccentricity e rotating at n rpm. Develop the differential form of Newtons equation of motion for the system. At what rotative speed will the amplitude of motion increase significantly. By means of a graph show how the rotational speed of the imbalance will affect the amplitudes of motion of the block.

Develop the differential form of Newtons equation of motion for the spring mass system indicated on the left. The mass meq is displacement is y1 and the wheel, which follows the road profile has a sinusoidal shape with maximum displacement y2.