Two springs with the same unstretched length, but different force constants k_1

Question

Two springs with the same unstretched length, but different force constants k_1 and k_2 are attached to a block with mass m on a level, frictionless surface. Calculate the effective force constant k(eff) in each of the three cases depicted in the figure . (The effective force constant is defined by F=-k(eff)x

a) Find k(eff) of a.

b) Find k(eff) of b.

c) Find k(eff) of c.

d)An object with mass m, suspended from a uniform spring with a force constant k, vibrates with a frequency f1. When the spring is cut in half and the same object is suspended from one of the halves, the frequency is f2. What is the ratio f2/f1

Explanation / Answer

a) k1 + k2 b)k1k2/(k1+k2) c)k1k2/(k1+k2) d)sqrt(2)

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