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A mass $M$ is tied to two springs, spring constants \(k_1,k_2\), 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 $(L_1+L_2)$, where $L_1,L_2$ are the natural lengths of the springs.
 
F
Write the Lagrangian for the following cases:
(a) The body is constrained to move only in a line along the springs.
(b) The body moves in a straight line only perpendicular to the springs.
(c) The body can move in any direction on the table.

 

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