Consider the following modification to the pendulum problem: a mass connected to the moving pivot A with a linear spring, with applied force F(t). The pivot point A moves with prescribed displacement x(t). Derive the two equations of motion of this system using vectorial mechanics. The natural (unstretched) length of the spring is Lo, and gravity is included. The applied force F(t) has constant horizontal direction. O x(t) g k F(t) L(t) m > X