Problem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a). Problem 1 (35 pts). An elastic string of constant line tension¹ T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.pv(x)XForce equilibrium in the string requires thatdf-p=0,dxwhere f(x) is the internal vertical force in the string, which is given bydvf=Tdx(1)(2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).

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Answered: Problem 1 (35 pts). An elastic string…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Problem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 and
x = L. A constant distributed vertical force per unit length p (with units N/m) is applied
to the string. Under this force, the string deflects by an amount v(x) from its undeformed
(horizontal) state, as shown in the figure below.
Force equilibrium in the string requires that
df
dx − p = 0 , (1)
where f(x) is the internal vertical force in the string, which is given by
f = T
dv
dx . (2)
(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.
(b) [2pts] What order is the governing PDE in the BVP of (a)?
(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).
(d) [20pts] Find the analytical solution of the BVP in (a).