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[QUE/CM-07002] Three Springs Problem

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Submitted by kapoor on Thu, 09/13/2018 - 22:40
Three massless springs of natural length $\surd 2$ and spring constant
      $k$ are attached to a point particle of mass $m$ and to the fixed
      points $(-1,1), (1,1)$ and $(1,1)$ as shown in the Fig. 1. The point
      mass is allowed to move in the $(x,y)$ plane only.

  1. Write the Lagrangian for the system.
  2. Is there an equilibrium position for the point mass? Where is it?
  3. Give the Lagrangian appropriate for small oscillations.
  4. Find the frequencies and normal coordinates of small oscillations.
  5. Sketch the normal modes.

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4727:Diamond Point

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