A \(30,000 \mathrm{~kg}\) locomotive is coupled to a fully loaded \(20,000 \mathrm{~kg}\) boxcar and moving at \(6.5 \mathrm{~m} / \mathrm{s}\). The assembly is coupled to a stationary and empty \(5,000 \mathrm{~kg}\) cattle car. The stiffness of each coupling is \(5.7 \times 10^{5} \mathrm{~N} / \mathrm{m}\).

(a) What are the natural frequencies of the three-car assembly?

(b) Mathematically describe the motion of the cattle car after coupling.