Problem 1) Design a surface to manage impact: Consider a mass M=2Kg that is dropped from a height of 0.5m (say from a conveyer belt) on to an elastic surface. To manage the impact you need to tailor the surface, which can be modeled as a parallel spring-damper system. Consider nominal values as K=1000N/m and C=50 N-s/m. Consider the downward direction as positive, and the un-deformed surface as displacement =0. 1) Find the position (time) response of the mass after it makes contact with the surface. (How would you find the initial conditions at the initial contact with the surface? Set this as time t=0.) Plot the response as a function of time. 2) Find the maximum displacement of the mass after it contacts the surface --- you can use simulations (e.g., MATLAB) to find the maximum. (Don't forget to add gravity force.) 3) Use simulations to find the maximum force (magnitude) on the mass after it contacts the surface. (Don't forget to include the gravity force.) 4) Change the spring constant K and/or damping constant C to reduce the maximum displacement of the mass M by half? Ensure that the mass does not lose contact with the surface. What happens to the maximum magnitude of the force with these changes? 5) Plot the displacement and force for the two cases (i.e., original K and C, and your new K and C) as a function of time and compare. Discuss the pros and cons of these two cases.