For a pendulum in a gravity field with point mass m and length L from mass to the pivot, derive the nonlinear equation of planar motion if theta is measured from the vertical (i.e., the equilibrium position theta_o = 0). Find the linear equation of motion that describes small oscillations about this equilibrium state. Repeat this problem (find both the nonlinear and linear equations of motion) for the same pendulum, but where theta is now measured from the horizontal (i.e., theta_o = 90 degrees = pi/2).