Figure 15.35 shows two weightless springs with springconstants k1 and k2 attached

Chapter 15, Problem 39

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Figure 15.35 shows two weightless springs with springconstants k1 and k2 attached between a ceiling and floorwithout tension or compression. A mass m is placed betweenthe springs which settle into equilibrium as in Figure15.36. The magnitudes f1 and f2 of the forces of thesprings on the mass minimize the complementary energyf 212k1+ f 222k2subject to the force balance constraint f1 + f2 = mg.(a) Determine f1 and f2 by the method of Lagrangemultipliers.(b) If you are familiar with Hookes law, find the meaningof .

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