Help Needed: Deriving Expressions for Mass-Spring System

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Discussion Overview

The discussion revolves around deriving expressions for a mass-spring system, specifically focusing on the equivalent spring constant (Keq) for springs in series. Participants seek assistance in understanding and deriving the relevant equations associated with this system.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant expresses difficulty in deriving the equations and identifies the first equation as a common expression for Keq in a mass-spring system in series.
  • Another participant suggests that the same reasoning used for the first equation can be applied to the other equations.
  • There is a discussion about the relationship between the tension in each spring, with a hint provided regarding this relationship.
  • One participant mentions the formula for tension in terms of spring constant and extension, indicating a connection between the extensions of the springs.
  • Clarification is sought regarding the definitions of x1 and x2, with one participant proposing that x1 represents the displacement of the end of spring one and x2 represents the displacement of the right side of spring two from its unstretched position.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the derivation process, as multiple viewpoints and uncertainties about the definitions and relationships between variables are expressed.

Contextual Notes

There are unresolved questions regarding the specific definitions of x1 and x2, as well as the steps needed to complete the derivation of the equations.

chocofingers
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Could somebody help me in deriving the following expressions?
I can judge that the first equation is a common expression for finding Keq for a mass-spring system in series.. Can't do the rest :/ anybody please ?

Thanks in advance.
 

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Show how you would derive the first equation. You'd use similar thinking for all three.
 
I don't know how to derive the first equation... If you could help me though for all the three... :)
 
You give it a try. Hint: What's the relationship between the tension in each spring?
 
Doc Al i gave it a try. I know the formulas ... tension(F) = k x e(extension) ...
so K1 e1 = K2 e2

Next what to do ?
 
chocofingers said:
I know the formulas ... tension(F) = k x e(extension) ...
so K1 e1 = K2 e2
Good! Now realize that e1 = x1 and e2 = x2 - x1.
 
what is x1 and x2 ? is x1 the extension of spring e1 ? then what is x2?
 
sorry i mean x2?
 
chocofingers said:
what is x1 and x2 ? is x1 the extension of spring e1 ? then what is x2?
I'd say (just from looking at the equation) that x1 is the displacement of the end of spring one from its unstretched position and x2 is the displacement of the right side of spring two from its unstretched position. Since the left side of spring one is fixed, x1 happens to equal the amount of stretch of spring one.
 

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