Solve equation (4) in Section 5.2 FIdywx) dxA (4) subject to the appropriate boundary conditions. The...
Solve equation (4) in Section 5.2 E = w(x) (4) subject to the appropriate boundary conditions. The beam is of length L, and wo is a constant. (a) The beam is embedded at its left end and simply supported at its right end, and w(x) = wg. 0<x<L. y(x) = (b) Use a graphing utility to graph the deflection curve when wo = 48E1 and L = 1. y + 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1...
Solve equation (4) in Section 5.2 ΕΙ = w(x) (4) dx4 subject to the appropriate boundary conditions. The beam is of length L, and wo is a constant. (a) The beam is embedded at its left end and free at its right end, and w(x) = Wo, 0<x<L. Wo y(x) = - 2Lx + 3 L’x) 24EI x (b) Use a graphing utility to graph the deflection curve when wo = 24EI and L = 1. X X 0.2 0.4...
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Question 3 A beam is embedded on its left side (x0) and simply supported on its right (L). Suppose the load on it is w(x) - wo- Compute the function of its deflection. (Note: embedded implies y(0) = 0 y'(0). Simply supported at x = L implies y(L)-0-y"(L)).
Question 3 A beam is embedded on its left side (x0) and simply supported on its right (L). Suppose the load on it is w(x) - wo- Compute...
der 5. (15 pts) Consider a homogeneous horizontal beam of length L. Recall that the deflection y (x)of such a beam satisfies the fourth order differential equation ELY wo where Wo is a constant load uniformly distributed along the length of the beam. The general solution of this equation is y () = C1 +223 + c3x2 + 423 + 2457 (a) Determine the appropriate boundary conditions if the beam is free on the left and embedded on the right...
5. (15 pts) Consider a homogeneous horizontal beam of length L. Recall that the deflection y (x) of such a beam satisfies the fourth order differential equation EI d'y - wo where wois a constant load uniformly d.24 distributed along the length of the beam. The general solution of this equation is y(x) = (1 + c2x + c3 x2 + 4x3 + 2001x4 (a) Determine the appropriate boundary conditions if the beam is free on the left and embedded...
dat 5. (15 pts) Consider a homogeneous horizontal beam of length L. Recall that the deflection y(x)of such a beam satisfies the fourth order differential equation Erd'y w where wois a constant load uniformly distributed along the length of the beam. The general solution of this equation is y(x) = c + C2# + 03 72 +423 + (a) Determine the appropriate boundary conditions if the beam is free on the left and embedded on the right (b) Solve the...
The next exercises consider different types of boundary conditions. 4. Suppose the concentration of pollutant is not allowed to leave the dam The diffusion equation (3.1.18) for the concentration in the dam still holds and the concentration at the river entrance is still ρ(0)-c, but the boundary condition at the dam wall must be changed to insist that there is no flux of pollutant leaving the dam. Construct the solution with this new boundary condition and plot the profile of...
help with all except numbers 21-26
16. Solve the differential equation by using the Cauchy-Euler Equation 17. Find the solution to the given Initial Value Problem using Green's Theorem 0,y'(0)s 0 y(0) y" + 6y' + 9y x, 18. Find the solution to the given Boundary Value Problem y" ty-1, y(O)0, y(1) 19. Solve the system of differential equations by systematic elimination. dy dt dt 20. Use any procedure in Chapter 4 to solve the differential equation subjected to the...
3. Consider the Laplace's equation on a rectangular domain subject to the following boundary conditions that represents the steady-state heating of a plate. A temperature probe shows that (1/2, 1/4) = 0. Solve this problem using the method of separation of variables. (7) byllyy = 0 0 <I<41 and O y <21 U-(0,y)=0, 1-(41, y) = cos(2), 4(1,0) = cos(2), 4(1,2)=0. (total 25 marks
2. We are lo solve y" -ky -) (O < x < L) subject to the boundary conditions y(0)y(L)0. a) Find Green's function by direct construction and show that for x ξ? b) Solve the equation G"- kG -(x - by the Fourier sine series method. is equivalent to the solution Can you show that the series obtained for G(x | found under (a)?
2. We are lo solve y" -ky -) (O