How Do You Calculate the Motion of an Object on a Sine Wave?

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SUMMARY

The discussion focuses on calculating the motion of an object on a sine wave, specifically in the context of water waves. Key factors include gravitational force (m*g) and buoyancy, which determines whether the object floats or sinks. If buoyancy exceeds gravitational force, the object oscillates vertically without horizontal movement. The conversation emphasizes the need for a mathematical equation to describe this motion accurately.

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  • Understanding of basic physics concepts such as gravitational force and buoyancy
  • Familiarity with sine wave properties and motion dynamics
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  • Basic calculus for deriving motion equations
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How would I go about calculating the motion of an object on a wave? For simplicity's sake let's just say its a sine wave. And this is an object on a water wave. Any pointers would be much appreciated. I'm interested in understanding how the mass of the object affect's it's motion in the vertical direction.
 
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In the context of water, gravitational force is m*g, while the water exerts a buoyancy force. If the buoyancy is stronger than gravity, then the object will move up and down in place while the waves in the water pass (keep in mind that objects that are floating don't actually move with the waves). Otherwise the object will sink.
 
zcd said:
In the context of water, gravitational force is m*g, while the water exerts a buoyancy force. If the buoyancy is stronger than gravity, then the object will move up and down in place while the waves in the water pass (keep in mind that objects that are floating don't actually move with the waves). Otherwise the object will sink.

Well i know all of these things but what I am interested in is an equation. Thanks for the help :)
 

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