P.2 0 mo F(t) 中 b m T kt bt Many systems, such as the Segway scooter, can be modeled using a modified version of the inverted pendulum. In the pictured problem, a mass mo is secured at the end of a massless rod of length 1. Use the constitutive relationship = 0 and 7 = b0. The torsional spring is undeformed when the pendulum is in its vertical, upright position. Note also that the mass is acted upon by a horizontal force F(t) Fosin wt. Use the Lagrangian approach to derive the equations of motion of the system.