The figure represents a simple pendulum with a string of length L of negligible mass compared to that of the attached weight at the end. The weight is initially pulled out 0, degrees from the vertical and then let go. If there is no air resistance, Newton's 2" law can be employed to calculate the time taken (period) for the weight to return to its starting position, i.e.: T = 4, dx , where T = time period, L = VI-k2 sin? x E. string length, 8 = acceleration due to gravity, and k = sin (0, /2). 1 =0 Problem: What string length is necessary (i.e. find L) in order for a Y W = mg pendulum with an initial pull angle of 0 = 30 to make exactly 10 complete swings per minute? Use Simpson's rule with n = 4 subintervals and get 2-decimal place accuracy for L (Note: 8 = 9.807 m/s-) path