3. The figure below shows the mass m with a shock-absorber assemny consisting of a plate of negligible mass, two springs with stiffness is, and a viscous damper with damping coefficient r. This system is initiallyI 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 it = 1 m, it contacts the rigid ground. The system's damped natural frequency is measured as fa = 5 Hz with if = 0.5. {a} Draw free-body diagrams and show that the general Eotu'l during contact can be stated as m? + c? + 2k? = mg. In this equation, Y represents the downward spring compression and the undefletted spring position is represented as Y = : lb} Determine the assemhiv's velocity at the time of contact with the ground: i-e.. find HI = }- lc} Find the displacement and velocity {Hz} and FM] of the system in contact with the ground and plot them. The :c-axis of Imur plot should be ranged from t = 0 to t = T; where 3'} is the time when the system loses the contact. Tr can be calculated by using a numerical approach such as a builtin function, "fsolve\" In Matlab or a function. 'fsolve" in the "sclpsroptlmize" library of Python. Submit your Matlab or Python code to generate the plot of Y and i". {de Find the peak amplitude of l" and the stopping time [when P' = 0]. Check your answers with the plot generated in Part [c]