In the two degree of freedom system shown below, the two thin uniform rods (each with mass m and length L) are horizontal in the static equilibrium position. HN HC 12 L4 01 31 a. (10 Pts) Show that the equations of motion are: [m .0 01 () CT [39 18 -k k 7 7 + 18 27 (02) 2 - 8 = k k 7 7 02 b. (7.5 Pts) Determine an upper limit for the lowest natural frequency using Rayleigh's quotient. Assume a trial vector of: (+) = (-15)} c. (7.5 Pts) Use Dunkerley's method to determine a lower bound for the lowest natural frequency.