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The array sonar is towed behind a surface ship on a long cylindrical cable that can be kilometers long. This keeps the array’s sensors away from the ship’s own noise sources, as shown in Fig. 2.

  • Initially, when the ship is at rest, the orientation of the ship, tow cable, and array is shown in Fig. 1.
  • When the ship starts moving at a constant speed, the cable and the sensor array attain an equilibrium, i.e., the cable and the array will maintain a fixed depth during the motion, as shown in Fig. 2.
  • The parameters which are known are: length, mass of cable and sensor array, the speed of the ship, and the density of water.
  • The cable is considered to be rigid, straight, and completely submerged in the water.
  • The cable is moving in XYZ space and the sensor array is moving in the XY plane.

The force balance equation can be used to solve the problem, but I'm new to this area so any help will be much appreciated.
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