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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 horizontal, frictionless track.

A block of mass M is connected to a spring of mass m and oscillates in simple harmonic motion on a horizontal, frictionless track. The force constant of the spring is k and the equilibrium length is l. Assume that all portions of the spring oscillate in phase and that the velocity of a segment dx is proportional to the distance x from the fixed end; that is, vx = (x/l)v. Also, note that the mass of a segment of the spring is dm = (m/l)dx.
Find the period of oscillation. (Use M, m, and k as necessary.)

This question was asked on Jan 18, 2013.

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