On page 2l2 ofour textbook, the model for a simple pendulum is shown to be: 63;? + sin t9 = 0 3" 7: d6 Assumeg = 32 , and != 2. Also assume 6(0) = E and d(O) = 0 .t (a) (10 points) The common assumption is that for 9 small, sinl9 E 9, so then the model becomes 2 i+6=0 dr 1 . . . . . . . . . 12' d9 Solve this Simplied model given the lnltlal conditions 6(0) = 3 and d(O) = 0 t 63 2.) (30 points) Using the cubic approximation; sin 6 E 6? from the Maclaurin series for sine, and a generic power series for 6 (centered at r: 0), 6" = 20\"!" , use the power series method to construct a H'{] sixth degree polynomial function for 6 that satises all ofthe conditions in the original model. 3.) (5 points) Sketch the graphs on the same coordinate system ot'both the function from part one, and the polynomial found in part two. Graph both for t e [E E]. f2