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Static equilibrium and minimum potential energy

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Deflection of springs. See attached file for full problem description.

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Solution Summary

The problem has been solved using statis equilibrium and minimum potential energy concepts.

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Please see the attached file.

Method 1 : Static equilibrium

Let us consider a small displacement ∆θ of the rod about the fulcrum under the action of the force F. Let the upper end of the rod be displaced by ∆x and the lower end by ∆y. The upper and lower springs will stretch by ∆x and ∆y respectively. Hence, the restoring forces developed in the springs will be :

F1 = k1∆y ......(1)
F2 = k2∆x ......(2)

For very small displacement, ∆θ ~ tanθ = ∆x/2L = ∆y/L .......(3)

Substituting from (3) in (1) and (2) :

F1 = ...

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