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Statement of a problem № 3488

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(a) A steel bar of density 7860 kg/m3 and Young's modulus 2x10^11 N/m2 and of length 0.25 m is rigidly clamped at one end and free to move at the other end. Determine the fundamental frequency of the bar for longitudinal harmonic vibrations. (b) How do the frequencies compare with (i) rod free at both ends; (ii) bar clamped at the midpoint; and (iii) bar clamped at both the ends.

Solution:
(a)  A steel bar of density 7860 kg/m3  and Young's modulus 2x10^11 N/m2 and of

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