if youo donot have matlab, then ignore plotting part

Given is the following system: Be L Figure 2: Problem setup a) Derive the equations of motion for this system, in order to gauge a tactical advantage over your opponent from the arts department. It can be assumed the system is in static equilibrium when the mass is in the center position as shown in the picture b) For the initial conditions x(0) = 1o and v(0) = vo derive the expressions for the underdamped, critically damped and overdamped case, in order to be able to best tune your shots. Assuming the mass is in the center of the table in the equilibrium position and the table is the standard size of 30 inches wide, the mass has 30 grams, a spring constant of 1.7 N/meter. c) what would the damping constant c need to be in order for critically damped, under- damped with damping parameter 5 = 0.5 and overdamped with damping parameter S= 1.5? What is the natural and damped frequency for all three cases? d) Make a matlab plot for all three cases mentioned in c), with an initial displacement of x(0)=5cm and an initial velocity of v(0=0.2cm/sec. i) make one plot for each case, plotting envelope functions, fast and slow root, where it applies. Explain all functions in the plots via accompanying text. ii) Make one plot with all three systems responses, explain the differences via ac- companying text. e) Name a system that can be represented by the problem setup. Given is the following system: Be L Figure 2: Problem setup a) Derive the equations of motion for this system, in order to gauge a tactical advantage over your opponent from the arts department. It can be assumed the system is in static equilibrium when the mass is in the center position as shown in the picture b) For the initial conditions x(0) = 1o and v(0) = vo derive the expressions for the underdamped, critically damped and overdamped case, in order to be able to best tune your shots. Assuming the mass is in the center of the table in the equilibrium position and the table is the standard size of 30 inches wide, the mass has 30 grams, a spring constant of 1.7 N/meter. c) what would the damping constant c need to be in order for critically damped, under- damped with damping parameter 5 = 0.5 and overdamped with damping parameter S= 1.5? What is the natural and damped frequency for all three cases? d) Make a matlab plot for all three cases mentioned in c), with an initial displacement of x(0)=5cm and an initial velocity of v(0=0.2cm/sec. i) make one plot for each case, plotting envelope functions, fast and slow root, where it applies. Explain all functions in the plots via accompanying text. ii) Make one plot with all three systems responses, explain the differences via ac- companying text. e) Name a system that can be represented by the problem setup