Excitation from unbalanced mass

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Discussion Overview

The discussion revolves around a physics problem involving a rigid body with an unbalanced mass that slides vertically within a frictionless prismatic pair, connected to a spring and a damper. The problem also includes a point mass rotating on a circular path, and participants are exploring how to relate vertical displacements to the rotational motion of the point mass.

Discussion Character

  • Homework-related
  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant expresses uncertainty about how to relate the vertical displacements of the rigid body to the rotational motion of the point mass.
  • Another participant suggests visualizing the problem and considers the effects of the rotating mass on the overall mechanism, comparing it to a washing machine model.
  • A later reply discusses the relationship between angular position and centrifugal force, indicating that the direction of the centrifugal force changes with the angular position of the mass.
  • Participants reference external resources that may provide similar problems and insights into the dynamics involved.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on how to approach the problem, with multiple viewpoints and suggestions being offered without resolution.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the system's dynamics and the need for further clarification on the equations of motion involved.

Godfather_bek
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Homework Statement


A rigid body of mass M slides vertically inside a friction-less prismatic pair. It is linked to the fixed frame through the spring of stiffness k, and a viscous damper with coefficient c. Beside the body, a point mass m rotates with constant speed w(omega) on a circular trajectory of radius r.(mass M also includes the point mass m)

Homework Equations


I don't know how to be with point mass. How to related vertical displacements with rotational? Can anyone suggest something..?

The Attempt at a Solution

 

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Examples this type of problem are to be found in many textbooks .

If you want to solve the problem yourself start by visualising the problem . When the eccentric mass is going around what do you expect to see the whole mechanism doing ?
 
Nidum said:
Examples this type of problem are to be found in many textbooks .

If you want to solve the problem yourself start by visualizing the problem . When the eccentric mass is going around what do you expect to see the whole mechanism doing ?
It is like washing machines model. If there was no rotating small mass, it would be much easier. How I realized it, as Ψ=Ωt and if Ψ is equal to Π/2, then centrifugal force Fc = mΩ2/r directed to upward. And if Ψ is -Π/2 it is downward. But how to be with equation of motion?
 

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