A cargo ship containing many boxes is at sea and experiences rough motion. Consider two masses in the cargo hold that are in close proximity when mass \(m_{1}\) is subjected to a force \(F=A \cos (\omega t+\phi)\) in line with the springs, as shown in Figure 6.72. The two masses are connected to each other via spring \(k_{2}\), and mass \(m_{1}\) is connected to the ship's hull via a spring and a damper. Derive the equation for the relative motion of the two masses.

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1+x F-A cos cot k 0.009 m 6000 m Figure 6.72: A two degree-of-freedom model of two masses on a cargo ship.