Determine the equation of motion for free vibration of the systems below. Ignore damping and masses of the members. EI L/2 m (a) u L/2 EI EI=00 m 2h EI ul (b) Determine the natural periods of the systems above if (L = 5 m, h= 2.5m, E = 25 GPa, I = 3e-3 m4, m= 100 tons) Study coulomb damping with viscous damping and comment on how the free vibration motion ends in two different damping mechanisms. If the frame in question 1(b) has a damping ratio of 7% and a force P(t) = (1kN)sinwt is applied when it is initially at rest (w=0.25wn), calculate its displacement response u(t), and plot on the u-t plane.