How can the natural frequency of a stationary cylinder be determined?

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Homework Help Overview

The discussion revolves around determining the natural frequency of a stationary cylinder, particularly in the context of its motion when displaced from equilibrium. The subject area includes concepts from mechanics and fluid dynamics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore modeling the position of the cylinder and question how to derive an equation for natural frequency when the cylinder is stationary. They discuss the forces acting on the cylinder when displaced and seek to form an equation of motion from these forces.

Discussion Status

The discussion is ongoing, with participants raising questions about the forces involved and how to mathematically express the net force on the cylinder. Some guidance is offered regarding Newton's 2nd Law, but no consensus or resolution has been reached.

Contextual Notes

Participants are considering the effects of gravity and buoyancy on the cylinder, and there is an emphasis on forming a mathematical expression for the forces involved. The original poster's approach is constrained by the need to model the situation accurately while adhering to the problem's requirements.

Ry122
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In this problem I guess I would first need to model the position of the cylinder with an equation and from that solve for the natural frequency. But how do I go about doing this when the object's default position is stationary?


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What is the force on the cylinder when it is displaced from its equilibrium position by a distance [itex]y[/itex] (up or down)?
 
It is equal to the weight of the water displaced I believe.
But how can I form an equation of motion from this?
 
Ry122 said:
It is equal to the weight of the water displaced I believe.

There are two forces acting on the cylinder at any given time:

(1) The downward force of gravity

(2) The buoyancy force (pressure) exerted by the water

Find a mathematical expression for the net force on the cylinder when it is displaced from equilibrium by a distance [itex]y[/itex]

But how can I form an equation of motion from this?

Newton's 2nd Law maybe?:wink:
 

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