1. The figure below shows the mass m with a shock-absorber assembly consisting of a plate of negligible mass, two springs with stiffness k, and a viscous damper with damping coefficient c. This system is initially held at rest at a height of h. It is then released, and the system moves down under gravity without friction. After moving the distance h = 1 m, it contacts the rigid ground. The system's damped natural frequency is measured as f = 5 Hz with 3 = 0.5. (a) Draw free-body diagrams and show that the general EOM during contact can be stated as m + c + 2kY = mg. In this equation, Y represents the downward spring compression and the undeflected spring position is represented as Y = 0. (b) Determine the assembly's velocity at the time of contact with the ground: i.e., find (t = 0). (c) Find the displacement and velocity (Y(t) and Y(t)) of the system in contact with the ground and plot them. The x-axis of your plot should be ranged from t = 0 tot = T where Tf is the time when the system loses the contact. T can be calculated by using a numerical approach such as a built-in function, "fsolve" in Matlab or a function, "fsolve" in the "scipy.optimize" library of Python. Submit your Matlab or Python code to generate the plot of Y and Y. (d) Find the peak amplitude of Y and the stopping time (when = 0). Check your answers with the plot generated in Part (c). g 50 m >kHck h