Coupled Oscillation attached at one end ?

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SUMMARY

The discussion focuses on determining the equation of motion for a system of two coupled oscillators as presented in the provided homework assignment. The key equation mentioned is x = Acos(ωt), which relates to the motion of oscillating masses. The participant emphasizes that while solving the differential equation is one approach, it may not be necessary if the task is solely to state the equations of motion. Additionally, the use of energy methods is noted but deemed unconventional for this specific problem.

PREREQUISITES
  • Understanding of coupled oscillations and their dynamics
  • Familiarity with the equation of motion for harmonic oscillators
  • Knowledge of energy conservation in spring-mass systems
  • Basic differential equations relevant to oscillatory motion
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Students studying classical mechanics, particularly those focusing on oscillatory motion and coupled systems, as well as educators seeking to clarify concepts related to equations of motion in physics.

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Homework Statement



I'm supposed to determine the equation of motion of the two masses on the worksheet. I just need to start with that. Here is the problem statement:
http://www.physics.udel.edu/~jim/PHYS211_14S/Homework%20assignments/Assignment%205%20-%20coupled%20oscillations.pdf



Homework Equations


I'm assuming x = Acos(ωt) has something to do with it as well as the energy of a spring-mass system
K + U.


The Attempt at a Solution



I don't know where to start. This is where I need the helping. Thank you for anyone who helps.
 
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It's very astute of you guessing the form of x. That is key to determining the solution of the differential equation. However, if the question is only asking for the equations of motion then I would interpret this to mean you don't have to solve the differential equation for x.

And although you could solve the problem using energy methods it is not usually the convention since this involves extra work that really isn't necessary I think in this case.
 

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