Given two rigid bars connected as shown. One of the bars has a mass M and the other M/2. The position shown is the static equilibrium position. a) (7 pts.) Derive the equations of motion in terms of k. M and L using any method you prefer. b) (3 pts.) Now set k-20 kN/m, M-40 kg and L=6 m. Determine the natural frequencies of the system. c) (Bonus; 5 pts.) Determine the mode shapes of the system. Hint: You need to write as many Lagrange's equations as there are degrees of freedom. L/3 M 21/3 M/2 L/2