The 25-ton engine of a steam locomotive is supported by suitable engine mounts within the structural framework of the locomotive. As the train travels over connected rails at its maximum speed, measurements indicate that the absolute maximum vibration amplitude of the framework is 10 mm, and the frequency of these vibrations can be approximated as a sinusoidal wave of 0.027 Hz. For the optimal performance of the engine, it is required that the maximum absolute amplitude of vibrations that the engine can undergo should be less than 5 mm. If the damping ratio of the mounting is 0.3, determine (a) the largest equivalent stiffness that the mountings need to have so that the engine operates within its optimal limits (7.5 marks) (b) the maximum deformations these mountings will undergo under such ideal operating conditions. (7.5 marks) (c) At what frequency of the frameworks vibration, as the train was picking up speed, was the engine operating at the least optimal conditions (i.e., the vibrations of the engine was at the maximum possible) (5 marks) (d) And at this worst-case scenario, how much percentage of the structural frameworks vibration amplitude was being transferred to the engine. (5 marks)