5.29 A representation of a car's suspension suitable for modeling the bounce and pitch motions is shown in Figure P5.29, which is a side view of the vehicle's body showing the front and rear suspensions. Assume that the car's motion is constrained to a vertical translation x of the mass center and rotation about a single axis which is perpendicular to the page. The body's mass is m and its moment of inertia about the mass center is Ig. As usual, x and 0 are the displacements from the equilibrium position corresponding to y = y2 = 0. The displacements yt and yo(t) can be found knowing the vehicle's speed and the road surface profile. a. Assume that x and are small, and derive the equations of motion for the bounce motion x and pitch motion e. b. For the values k = 1100 lb/ft, k = 1525 lb/ft, c = c = 4 lb-sec/ft, L = 4.8 ft. L2 = 3.6 ft, m = 50 slugs, and Ig = 1000 slug-ft, use MATLAB to obtain a state-variable model in standard form. c. Use MATLAB to obtain and plot the solution for X(t) and e(t) when y = 0 and y2 is a unit impulse. The initial conditions are zero. It LG Front Road surface Rear ki 5.29 A representation of a car's suspension suitable for modeling the bounce and pitch motions is shown in Figure P5.29, which is a side view of the vehicle's body showing the front and rear suspensions. Assume that the car's motion is constrained to a vertical translation x of the mass center and rotation about a single axis which is perpendicular to the page. The body's mass is m and its moment of inertia about the mass center is Ig. As usual, x and 0 are the displacements from the equilibrium position corresponding to y = y2 = 0. The displacements yt and yo(t) can be found knowing the vehicle's speed and the road surface profile. a. Assume that x and are small, and derive the equations of motion for the bounce motion x and pitch motion e. b. For the values k = 1100 lb/ft, k = 1525 lb/ft, c = c = 4 lb-sec/ft, L = 4.8 ft. L2 = 3.6 ft, m = 50 slugs, and Ig = 1000 slug-ft, use MATLAB to obtain a state-variable model in standard form. c. Use MATLAB to obtain and plot the solution for X(t) and e(t) when y = 0 and y2 is a unit impulse. The initial conditions are zero. It LG Front Road surface Rear ki