Chapter 14, Problem 14.92CP

The Effective Force Constant of Two Springs. Two springs with the same unstretched length hut different force constants k₁ and k₂ 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 (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?

Figure P14.92