2. (25pts) The equation of motion of a pendulum is given by the following: dt2 + L sin (0) = 0, where g =9.8, the gravitational constant on Earth, and let L = 0.6, the lenght of the pendulum. (a) Use Euler's method with a step-size of 1/3 to approximate #(1) and 0(2) if e(0) = x/6 and e(0) = 0. (b) To simplify the equation, many lecturers use the small-angle approximation. They approximate the function sin(0) as a Taylor polynomial of order 2 about 0. Show that it is equivalent to dt2 + LA = 0. L (c) Redo part (a) but for the differential equation in (b). (d) Is the small-angle approximation good for our intial value