A particle of mass 1.18 kg is attached between two identical springs on a horizontal frictionless tabletop. The springs have force constant k and each is initially unstressed. (a) If the particle is pulled a distance x along a direction perpendicular to the initial configuration of the springs, as in Figure P8.47, show that the potential energy of the system is (Hint: See Problem 58 in Chapter 7.) (b) Make a plot of U(x) versus x and identify all equilibrium points. Assume that L = 1.20 m and k = 40.0 N/m. (c) If the particle is pulled 0.500 m to the right and then released, what is its speed when it reaches the equilibrium point x = 0?

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L I Top View Figure P8.47