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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