Question: 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

Determine the equation of motion for free vibration of the systems below.

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.

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