A block of mass M is connected to a spring of mass m and

Chapter 15, Problem 87

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A block of mass M is connected to a spring of mass m and oscillates in simple harmonic motion on a frictionless, horizontal track (Fig. P15.87). The force constant of the spring is k, and the equilibrium length is ,. Assume all portions of the spring oscillate in phase and the velocity of a segment of the spring of length dx is proportional to the distance x from the fixed end; that is, vx 5 (x/,)v. Also, notice that the mass of a segment of the spring is dm 5 (m/,)dx. Find (a) the kinetic energy of the system when the block has a speed v and (b) the period of oscillation.

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