Determine the fundamental frequency of the bar

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Reference no: EM13709703

A bar of length L is rigidly fixed at x=0 and free to move at x=L.

a. show that only odd integral harmonic overtones are allowed

b. determine the fundamental frequency of the bar, if it is composed of steel and has a length of 0.5m.

c. If a static force F is applied to the free end of the bar so as to displace this end by h, show that, when the bar vibrates longitudinally subsequent to the sudden release of this force, the amplitudes of the various vibrations are given by A_n= [(8h) / (npi)^2]sin(npi/2)

d. determine these amplitudes for the above steel bar, if the force is 5000 N and the cross-sectional area of the bar is 0.0005 m^2.

Reference no: EM13709703

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