What are the key steps for drawing a mass-spring free body diagram?

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Discussion Overview

The discussion revolves around the process of drawing a free-body diagram for a system involving two equal masses connected by three springs on a frictionless table. Participants explore the forces acting on the masses and the setup of equations of motion for the system.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant describes a system with two masses and three springs, questioning the forces acting on each mass and whether to include both wall spring forces in the free-body diagram.
  • Another participant clarifies that each mass experiences two spring forces due to its connections to the springs.
  • Further contributions emphasize that in equilibrium, all three springs will exhibit the same extension or deflection.
  • Participants discuss the horizontal displacements Y1 and Y2 for the masses, with Y1 representing the displacement of the first mass and Y2 for the second mass.
  • Equations of motion are proposed for both masses, with one participant expressing uncertainty about the inclusion of displacement terms (d1 and d2) in the equations.
  • Another participant suggests that the displacement terms may not be necessary, arguing that the deflections can be represented by the differences in displacements between the masses.
  • One participant shares their background as a 50-something engineering master's student, indicating a struggle with the material after a long time since their undergraduate studies.

Areas of Agreement / Disagreement

Participants generally agree that each mass is influenced by two spring forces. However, there is disagreement regarding the necessity of including displacement terms in the equations of motion, with some participants asserting they are unnecessary while others do not explicitly resolve this uncertainty.

Contextual Notes

The discussion includes assumptions about the system being in equilibrium and the nature of the spring constants and masses being equal. There is also a lack of consensus on the treatment of displacement terms in the equations of motion.

Who May Find This Useful

This discussion may be useful for students or individuals studying dynamics, particularly those working on problems involving mass-spring systems and free-body diagrams.

dondiego
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I am trying to get started on a problem. I have two masses M1 = M2 and three springs all with the same constant. The weights and springs are on a frictionless table and the outer springs are attached to walls

Wall ~~~Mass~~~Mass~~~Wall

How do I draw the free-body diagram? I am confused about the forces. I know each mass has a spring force pulling it towards the wall and the middle spring should be a force on each mass in the opposite direction that the wall spring force is. Are these the only forces? Or do I need to show both wall spring forces on each mass?
 
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Each mass connects to two springs and thus has two spring forces acting on it.
 
Yeah for each mass two spring forces are acting on it...thats all...
so for equilibrium and same spring constants and masses ... alll 3 springs will show same extension/deflection...
 
R Power said:
Yeah for each mass two spring forces are acting on it...thats all...
so for equilibrium and same spring constants and masses ... alll 3 springs will show same extension/deflection...

So I need to find the horizontal displacements Y1 and Y2 with Y1 the displacement on the first mass in the right direction and Y2 the displacement on the 2nd mass in the right direction.

The motion is started from rest with Y(0) = [1 1] and Y'(0) = [0 0]

Y(0) and Y'(0) should be vertical vectors, i.e one column but I did not know how to represent them that way.


I am also given that M=3kg and K=9N/m

I just want help in setting it up. I am coming up with these two equations but I don't know if it is right:

For the first mass -k(y1 +d1) + k(y2-y1+d2) = my''
For the 2nd mass -k(y2-y1+d1) + k(y2+d2) = my''

I'm not sure whether I should have the d terms in there or not (d is displacement) since they are starting at rest.
 
Last edited:
the d terms need not be there i think...then the equations seem correct.
Yeah! no d terms I'm pretty sure!

Reason: (y2 - y1) itself is the deflection of the second spring (starting from left) and y1 is the displacement of the first spring. So there is no way these extra d1 and d2 come from.

Actually I mean- d2= y2 - y1
d1= y1
 
Last edited:
R Power said:
the d terms need not be there i think...then the equations seem correct.
Yeah! no d terms I'm pretty sure!

Reason: (y2 - y1) itself is the deflection of the second spring (starting from left) and y1 is the displacement of the first spring. So there is no way these extra d1 and d2 come from.

Actually I mean- d2= y2 - y1
d1= y1

Thanks. I'm still working on it but that helps. I'm a 50 something engineering masters student and this stuff is not coming back to me very easy as it's been a long time since I got my BS. Of course back then, resources like this weren't here either!

Thanks!
 

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