2. (15 points) Consider the internal combustion engine m shown below that is attached to the automobile frame via elastic mounts that are modeled here as springs with stiffness k. The vibration induced by the reciprocating parts of the engine is modeled as the external force f and the automobile frame can be considered as fixed. One approach to reducing the vibration induced by the engine on the frame is to connect a second smaller mass m to the primary mass via an elastic member modeled here as having stiffness k2 and damping b. Write the differential equation(s) that govern the behavior of this system as described. Engine (m) - x k k M 2 k x2 absorber rigid base