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

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To calculate the motion of an object on a sine wave, one must consider the forces acting on it, specifically gravitational force and buoyancy. The gravitational force is determined by the object's mass (m) multiplied by the acceleration due to gravity (g). If the buoyancy force exceeds the gravitational force, the object will oscillate vertically in place as the wave passes, while a weaker buoyancy will cause it to sink. The discussion emphasizes the need for a specific equation to model this motion effectively. Understanding these dynamics is crucial for accurately predicting the object's behavior on a water wave.
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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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