Problem 5. (10 points) A heavy machine, weighing 3000 N, is supported on a resilient foundation. The static deflection of the foundation due to the weight of the machine is found to be 7.5 cm. It is observed that the machine vibrates with an amplitude of 1 cm when the base of the foundation is subjected to harmonic oscillation at the undamped natural frequency of the system with an amplitude of 0.25 cm. Find: a. The damping constant of the foundation. b. Amplitude of the dynamic force transmitted to the base. c. The amplitude of the displacement of the machine relative to the base.