Derive the equation of motion for the axial rod that is attached to a spring k atx=0 and free at x=L. Its mass per unit length is m(x), cross sectional area is A(x)and is subjected to force per unit length f(x,t), E is the modulus of elasticity.Derive the boundary value problem with the boundary conditions.u(x,t)(x,t)kт(x), EA(х)LFor the problem 3, m(x) = m(1- x/2L), EA(x) = EA(1 - x/2L) k = EA/2L. UseRayleigh-Ritz method and the trial functions 4(x) = Cos inx / L i=0,1,2; to findthe natural frequencies of the system.For the same problem if f(x,t) = Fosin ot d(x-L) (Harmonic point force located atx=L), determine the system response using assumed modes method. Use thesame trial functions as in problem 4.

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Derive the equation of motion for the axial rod that is attached to a spring k at x=0 and free at x=L. Its mass per unit length is m(x), cross sectional area is A(x) and is subjected to force per unit length f(x,t), E is the modulus of elasticity. Derive the boundary value problem with the boundary conditions. u(x,t) f(x,t) k т(x), EA(х) L For the problem 3, m(x) = m(1- x/2L), EA(x) = EA(1 - x/2L) k = EA/2L. Use Rayleigh-Ritz method and the trial functions (x) = Cos inx / L i=0,1,2; to find the natural frequencies of the system. For the same problem if f(x,t) = Fosin ot 8(x-L) (Harmonic point force located at x=L), determine the system response using assumed modes method. Use the same trial functions as in problem 4.

Derive the equation of motion for the axial rod that is attached to a spring k at x=0 and free at x=L. Its mass per unit length is m(x), cross sectional area is A(x) and is subjected to force per unit length f(x,t), E is the modulus of elasticity. Derive the boundary value problem with the boundary conditions. u(x,t) f(x,t) k т(x), EA(х) L For the problem 3, m(x) = m(1- x/2L), EA(x) = EA(1 - x/2L) k = EA/2L. Use Rayleigh-Ritz method and the trial functions (x) = Cos inx / L i=0,1,2; to find the natural frequencies of the system. For the same problem if f(x,t) = Fosin ot 8(x-L) (Harmonic point force located at x=L), determine the system response using assumed modes method. Use the same trial functions as in problem 4.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

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Derive the equation of motion for the axial rod that is attached to a spring k at
x=0 and free at x=L. Its mass per unit length is m(x), cross sectional area is A(x)
and is subjected to force per unit length f(x,t), E is the modulus of elasticity.
Derive the boundary value problem with the boundary conditions.
u(x,t)
(x,t)
k
т(x), EA(х)
L
For the problem 3, m(x) = m(1- x/2L), EA(x) = EA(1 - x/2L) k = EA/2L. Use
Rayleigh-Ritz method and the trial functions 4(x) = Cos inx / L i=0,1,2; to find
the natural frequencies of the system.
For the same problem if f(x,t) = Fosin ot d(x-L) (Harmonic point force located at
x=L), determine the system response using assumed modes method. Use the
same trial functions as in problem 4.

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