A new spar buoy, 0.5 m diameter, is being designed to carry oceanographic instrumentation in the Indian Ocean. At this stage in the design process, the heave motion of the buoy is being modeled as a simple spring-mass-damper system. The current design has an effective mass (a + m) of 650 kg. The design includes 200 kg of lead ballast in this mass. The restoring force is the change in buoyancy as the buoy heaves. The damping for a cylinder of this size is estimated to be 0.28 kN-sec/m. The wave-induced exciting force is assumed to have the form of a sine function with an amplitude of 1.65 kN and a frequency of 0.8 rad/sec. For this wave condition it is desired to keep the maximum amplitude of the motion to less than 1 m. The only flexibility in the design is the amount of lead ballast. You can have either 0, 200, or 400 kg of ballast. What is your choice and why?

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