Problem 1. A diving board is made of aircraft aluminum alloy (Young's Modulus is 69 GPa, density of aluminum alloy 2700\text{kg/}{{\text{m}}^{\text{3} }}2700kg/m 3 ) with the dimension of 16 feet long, 20 inches wide, and 1 5/8 inch high. The fulcrum point is located at 8 feet from the tip. 1) Find the equation of motion of the system. Hint: treat the diving board to be a cantilever beam clamped at the fulcrum point. State the assumption(s) used to derive the solution, and discuss if the assumption is valid. What error results from the assumption(s) made