Determine the free vibration response of the railroad bridge of Chapter Problem 8.14 if a ground disturbance initially leads to \(\theta_{1}=0.8^{\circ}\) with \(\theta_{2}=\theta_{3}=0\).

Data From Chapter Problem 8.14:

A \(500 \mathrm{~kg}\) machine is placed at the end of a \(3.8-\mathrm{m}-\mathrm{long}, 190-\mathrm{kg}\) fixed-free beam. The beam is made of a material of elastic modulus \(200 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\) and has a cross-sectional moment of inertia of \(1.4 \times 10^{-5} \mathrm{~m}^{4}\). Use a three degree-of-freedom model to approximate the two lowest natural frequencies of the system.