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Unformatted text preview: 15.53: a) See Exercise 15.10; a y = 2 y t 2 = -2 y, and so k = m2 = x 2 .
2 b) 4 2 F 2v 2 2 = ( 2f ) = = 2 and so k = (4 2 F 2 )x. The effective force constant k is independent of amplitude, as for a simple harmonic oscillator, and is proportional to the tension that provides the restoring force. The factor of 1 2 indicates that the curvature of the string creates the restoring force on a segment of the string. More specifically, one factor of 1 is due to the curvature, and a factor of 1 () represents the mass in one wavelength, which determines the frequency of the overall oscillation of the string. The mass m = x also contains a factor of , and so the effective spring constant per unit length is independent of . ...
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