. An inverted pendulum is supported by a linear spring, as shown in Fig. 1.76. It is required to: (a) Derive the equation for the angular motion 6(r) about O. (b) Determine the equilibrium positions. (c) Derive the differential equation for small and lar motions (1) about 6 for each equi- librium position. (d) Determine the stability nature of each equilibrium position. k m www FIGURE 1.76 Inverted pendulum supported by a spring