Two springs with the same unstretched length but different force constants k₁and k₂are attached to a block with mass m on a level, frictionless surface. Calculate the effective force constant k_effin each of the three cases (a), (b), and (c) depicted in Fig. P14.92. (The effective force constant is defined by ΣF_x= -k_effx.) (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 f₁/f₂?

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(a) (b) k1 (c) k1 k2