How Does Spring Configuration Limit Mass Movement in Physics?

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Homework Help Overview

The discussion revolves around a mass connected to two springs in a room, exploring how the configuration of these springs affects the mass's movement. The original poster seeks to understand the limitations on the mass's movement based on its initial conditions and the force vector F(x,y).

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants inquire about the nature of the force vector F(x,y) and whether it represents the force from the springs or another source. There is also a suggestion to consider the governing differential equations of the mass's motion.

Discussion Status

The discussion is ongoing, with participants clarifying definitions and exploring the implications of the spring forces on the mass's trajectory. Some guidance has been offered regarding the relationship between initial velocities and the path of the mass.

Contextual Notes

Participants are working with the assumption that the mass is initially at rest and are considering the effects of spring forces in a two-dimensional space. There is an emphasis on understanding the governing equations of motion without providing explicit solutions.

cscott
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Homework Statement




Say you have a mass in the center of a room (equilibrium (x,y) = (0, 0)) that is connected to one wall via a spring along -x axis and to another wall via a spring along -y axis (the axes are parallel with each wall, respectively.) If I know F(x,y) and the velocity at a point, after the mass is set in motion with an initial velocity at some other point is there any way to figure out which region of the floor the mass will be restricted to?

The Attempt at a Solution



No ideas here...
 
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What is F(x,y) supposed to be?
 
Avodyne said:
What is F(x,y) supposed to be?

F(x,y) = force vector

sorry.
 
Is F the force produced by the springs, or some other force?
 
By the springs
 
cscott said:

Homework Statement




Say you have a mass in the center of a room (equilibrium (x,y) = (0, 0)) that is connected to one wall via a spring along -x axis and to another wall via a spring along -y axis (the axes are parallel with each wall, respectively.) If I know F(x,y) and the velocity at a point, after the mass is set in motion with an initial velocity at some other point is there any way to figure out which region of the floor the mass will be restricted to?
Yes, you can know the path of the mass if you know two velocities, and you also know both components of F(x,y).

Can you write down the differential equations governing the motion of the mass in (x,y)?
 

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