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6. (a) Calculate the first three frequencies of axial vibration of a bar fixed at one...

6. (a) Calculate the first three frequencies of axial vibration of a bar fixed at one end.

       (b) Derive the orthogonality condition of natural modes of vibration in axial direction.                                                                                              

         (c)   Discuss the modal analysis method.                                                  

        (d). Determine the first two frequency by Rayleigh-ritz method, assuming

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