A spool of mass m = 200 kg, radius r = 0.8 m, and radius of gyration kG = 0.65 m rolls wit...

A spool of mass m = 200 kg, radius r = 0.8 m, and radius of gyration kG = 0.65 m rolls without slipping on the incline, whose angle with respect to the horizontal is θ = 38°. A linear elastic spring with constant k = 500 N/m and unstretched length L0 = 1.5 m connects the center of the spool to a fixed wall. Determine the equation(s) of motion of the spool, using the x coordinate shown; solve them for 15 s, using the initial conditions x(0) = 2.5 m and ẋ(0) = 0 m/s; and then plot x versus t. What is the approximate period of oscillation of the spool?

Figure P7.52