The overhead trolley shown in Figure is used to transport beams in a factory. The beam is rectangular, with a length of L. It is desired to limit the trolley horizontal acceleration a so that the beam does not swing too much. The beam starts from rest with θ(0) = 0. (a) Use a small angle approximation and determine the maximum value of θ if L = 3 m and a = 2 m/s2. Once you obtain an answer, use it to check the validity of the small angle approximation, (b) Solve the problem given in part (a), using symbolic values for L, a, and g. Does the answer depend on all three variables? If not, explain why.