ME 163 Engineering Mechanics: Vibrations. Final Exam

The assembly shown on the right is in a configuration where the springs are unstretched. Assume small lateral motions around this configuration and no vertical motion. Find the natural frequency of this system in terms of m, k1 and k2.Problem 2 k k ke↵ m m f(t) c c ce↵ On the right is a diagram of a simplified engine mount design problem. The values of the two mounting springs’ constant k and dampers c is to be determined. It is known that a 300 Kg engine is slightly imbalanced, and the worst vibrations occur at idle speed of 900 rpm. It is decided that the damping ratio for the whole system should be ζ = 0.1. The whole system is modeled as a single mass m supported by an equivalent spring keff and damper ceff. The engine imbalance is modeled as an oscillatory force f(t) with the same frequency as the engine’s rpm. The plot below shows the ratio of the mass’ oscillation amplitude divided by the static sag for a forced Spring-Mass-Damper system when ζ = 0.1 What should k and c be so that the engine’s oscillation amplitude at idle is no larger than 40% of the static sag?Problem 3 A : B : m k c Consider the mass-spring-damper system shown on the right in two different configurations. In configuration A, the spring is unstretched. The width of the mass is 10 cm. m = 1 Kg, and k = 100 N/m. The damping coefficient c is to be designed. Suppose the mass starts at rest in configuration B. What is the minimum value of c needed so that the amplitude of oscillation after 2 seconds is at most 1 mm.