Every mechanical system can be modeled by an inertia-spring-dashpot system. The inertia element represents the total mass of the system. The spring shows how elastic the system is. The dashpot reveals the energy loss mechanism in the system (for example due to friction). The boom AB of the crane shown in Fig.-1 is a uniform steel bar of length 10 m and area of cross section 2500 mm. A weight W is suspended while the crane is stationary. The cable CDEBF is made of steel and has a cross-sectional area of 100 mm. Neglecting the effect of the cable CDEB. 1.5 mi 11.5m W Fig. 1-Crane lifting a load. Suppose the system has no mechanism for loosing energy (no dashpot or c = 0). a) find the equivalent spring constant of the system in the vertical direction. b) Drive the ordinary differential equation (ODE) of motion for the vibration of the weight. c) Solve the ODE and find the vibration of the vehicle, x(7), at any instant of time, I. d) How would your answer in part e be different if the crane has a viscous damping. mechanism with c= 100 N.s/m. compare your answers by plotting x-1 curves for parts c and d.