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Solve the eigenvalue problem for the "fixed-free" uniform elastic rod in extension. The rod has density ρ, cross-sectional area A, elastic modulus E, and length L. Then, determine the first four modes and sketch the corresponding mode shapes.

          Solve the eigenvalue problem for the "fixed-free" uniform elastic rod in extension. The rod has density ρ, cross-sectional area A, elastic modulus E, and length L. Then, determine the first four modes and sketch the corresponding mode shapes.
        
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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Solve the eigenvalue problem for the "fixed-free" uniform elastic rod in extension. The rod has density ρ, cross-sectional area A, elastic modulus E, and length L. Then, determine the first four modes and sketch the corresponding mode shapes.
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Transcript

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00:01 Hello students, in this question given as a diameter of wire is 10 mm.
00:05 So, this will be equal to the 10 to the power minus 2 meter and the elasticity constant is equal to 100 giga pascal.
00:17 Length of the wire is 4 meter and applied load on the wire is 6 kilo newton.
00:27 Now we have to find the elongation in the wire.
00:31 So, the formula is elongation in the wire is equal to load into l upon area cross sectional area of the wire into elasticity constant...
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