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A mass \(M\) is tied to two springs and lies on a smooth horizontal table as shown in figure. The free ends of the springs are held fixed at points separated by a distance \(L1+L_2\) where \(L1, L2\) are the natural lengths of the springs. Write the Lagrangian for the following cases:
  • The body is constrained to move only in a line along the springs.
  • The body moves in a straight line only perpendicular to the springs.
  • The body can move in any direction on the table.
Two springs and a mass.

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