Homework Answers
Any query in any step then comment below. I will explain you..
According to rules and regulations, we are able to do only one question at a time.. so I do question 11th.
9) Solve the following partial differential equation au a2u ax2 n(0, t) = u(2, t)-0 t > 0 (x, 0) = 0 au at It=0 =x(2-x) 9) Solve the following partial differential equation au a2u ax2 n(0, t)...
9) Solve the following partial differential equation au a2u ax2 n(0, t) = u(2, t)-0 t > 0 (x, 0) = 0 au at It=0 =x(2-x)
9) Solve the following partial differential equation au a2u ax2 n(0, t) = u(2, t)-0 t > 0 (x, 0) = 0 au at It=0 =x(2-x)
governed by the wave equation, Torsional vibration of a shaft at2 ax2 where x, t) is the angular displacement (angle of...
governed by the wave equation, Torsional vibration of a shaft at2 ax2 where x, t) is the angular displacement (angle of twist) along the shaft, x is the distance from the end of the shaft and t is time. For a shaft of length 4T that is supported by frictionless bearings at each end, the boundary conditions are t > 0 ex(0, t) 0x(47, t) = 0, Suppose that the initial angular displacement and angular velocity are e(x,0) = 3...
a) Use the d'Alembert solution to solve au au - <r< ,t> 0, at2 48,2 ux,0)...
a) Use the d'Alembert solution to solve au au - <r< ,t> 0, at2 48,2 ux,0) = cos 3x, u(,0) = 21 b) Consider the heat equation диди 0<x<1, t > 0, at ax? with boundary conditions uz (0,t) = 0, uz(1,t) = 0, > 0, and initial conditions u(x,0) = { 0, 2.0, 0<r < 0.5, 0.5 <<1. Use the method of separation of variables to solve the equation.
solve the PDE +u= at2 on 3 € (0,L), t > 0, with boundary conditions au...
solve the PDE
+u= at2 on 3 € (0,L), t > 0, with boundary conditions au 2x2 u(0,t) = 0, u(L, t) = 0 au and initial condition u(x,0) = f(x), at (x,0) = g(x) following the steps below. (a) Separate the variables and write differential equations for the functions (x) and h(t); pick the separation constant so that we recover a problem already studied. (b) Find the eigenfunctions and eigenvalues. (c) Write the general solution for this problem. (d)...
In each of Problems 1 through 8, solve the initial-boundary value problem using separation of variables....
In
each of Problems 1 through 8, solve the initial-boundary value
problem using separation of variables. Graph the fiftieth partial
sum of the solution for some values of t. with c = 1 if c is
unspecified in the problem.
a2y = 4- for 0< x <3, t >0 1. at2 ax2 y(0, t)=y(3, t)=0 for t 0 y(x, 0) (x, 0) = x (3- x) for 0x3 0, at a2y yfor 0 <x < 4, t > 0 4....
b) Consider the wave equation azu azu at2 0 < x < 2, t>0, ar2 with...
b) Consider the wave equation azu azu at2 0 < x < 2, t>0, ar2 with boundary conditions u(0,t) = 0, u(2, t) = 0, t> 0, and initial conditions u(x,0) = x(2 – x), ut(x,0) = = 0, 0 < x < 2. Use the method of separation of variables to determine the general solution of this equation. (15 marks)
Question 1 - 16 Consider the following intial-boundary value problem. au au 0<x< 1, 10, at2...
Question 1 - 16 Consider the following intial-boundary value problem. au au 0<x< 1, 10, at2 ax?' u(0,t) = u(11,t) = 0, 7>0, u(x,0) = 1, 34(x,0) = sin10x + 7sin50x. (show all your works). A) Find the two ordinary differential equations (ODES). B) Solve these two ODES. Show all cases 1 <0, 1 = 0, and > 0 C) Write the complete solution of this initial - boundary value problem.
au (x, at2 a (2,t), 0 < x < 57, to ac2 u(0,t) = 0, u(57,...
au (x, at2 a (2,t), 0 < x < 57, to ac2 u(0,t) = 0, u(57, t) = 0, t>0, u(3,0) = sin(4x), ut(x,0) 4 sin(5x), 0 < x < 57. u(x, t) =
Solve using the Laplace Transform the problem with border values au x2 au at2 para 0<x<1,7...
Solve using the Laplace Transform the problem with border
values
au x2 au at2 para 0<x<1,7 > 0 sujeto a las condiciones u(0,t) = 0, u(,0) = 0, ди u(1,t) = 0 2 sin(72) + 4 sin(372) at lt=0
d1=8 d2=9 lu for Find the solution u(x,t) for the l-D wave equation-=- Qx2 25 at2 (a) oo < x < oo with initial conditions u(x,0)-A(x) , where A(x) Is presented in the diagram below, and zero in...
d1=8
d2=9
lu for Find the solution u(x,t) for the l-D wave equation-=- Qx2 25 at2 (a) oo < x < oo with initial conditions u(x,0)-A(x) , where A(x) Is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and t, somewhat similar to f(x) on page 85 of the Notes Part 2. d2+5 di+10 di+15dı+20 (b) Check for the wave equation in (a) that if (x...
9) Solve the following partial differential equation au a2u ax2 n(0, t) = u(2, t)-0 t > 0 (x, 0) = 0 au at It=0 =x(2-x)
9) Solve the following partial differential equation au a2u ax2 n(0, t) = u(2, t)-0 t > 0 (x, 0) = 0 au at It=0 =x(2-x)
governed by the wave equation, Torsional vibration of a shaft at2 ax2 where x, t) is the angular displacement (angle of twist) along the shaft, x is the distance from the end of the shaft and t is time. For a shaft of length 4T that is supported by frictionless bearings at each end, the boundary conditions are t > 0 ex(0, t) 0x(47, t) = 0, Suppose that the initial angular displacement and angular velocity are e(x,0) = 3...
a) Use the d'Alembert solution to solve au au - <r< ,t> 0, at2 48,2 ux,0) = cos 3x, u(,0) = 21 b) Consider the heat equation диди 0<x<1, t > 0, at ax? with boundary conditions uz (0,t) = 0, uz(1,t) = 0, > 0, and initial conditions u(x,0) = { 0, 2.0, 0<r < 0.5, 0.5 <<1. Use the method of separation of variables to solve the equation.
solve the PDE
+u= at2 on 3 € (0,L), t > 0, with boundary conditions au 2x2 u(0,t) = 0, u(L, t) = 0 au and initial condition u(x,0) = f(x), at (x,0) = g(x) following the steps below. (a) Separate the variables and write differential equations for the functions (x) and h(t); pick the separation constant so that we recover a problem already studied. (b) Find the eigenfunctions and eigenvalues. (c) Write the general solution for this problem. (d)...
In
each of Problems 1 through 8, solve the initial-boundary value
problem using separation of variables. Graph the fiftieth partial
sum of the solution for some values of t. with c = 1 if c is
unspecified in the problem.
a2y = 4- for 0< x <3, t >0 1. at2 ax2 y(0, t)=y(3, t)=0 for t 0 y(x, 0) (x, 0) = x (3- x) for 0x3 0, at a2y yfor 0 <x < 4, t > 0 4....
b) Consider the wave equation azu azu at2 0 < x < 2, t>0, ar2 with boundary conditions u(0,t) = 0, u(2, t) = 0, t> 0, and initial conditions u(x,0) = x(2 – x), ut(x,0) = = 0, 0 < x < 2. Use the method of separation of variables to determine the general solution of this equation. (15 marks)
Question 1 - 16 Consider the following intial-boundary value problem. au au 0<x< 1, 10, at2 ax?' u(0,t) = u(11,t) = 0, 7>0, u(x,0) = 1, 34(x,0) = sin10x + 7sin50x. (show all your works). A) Find the two ordinary differential equations (ODES). B) Solve these two ODES. Show all cases 1 <0, 1 = 0, and > 0 C) Write the complete solution of this initial - boundary value problem.
au (x, at2 a (2,t), 0 < x < 57, to ac2 u(0,t) = 0, u(57, t) = 0, t>0, u(3,0) = sin(4x), ut(x,0) 4 sin(5x), 0 < x < 57. u(x, t) =
Solve using the Laplace Transform the problem with border
values
au x2 au at2 para 0<x<1,7 > 0 sujeto a las condiciones u(0,t) = 0, u(,0) = 0, ди u(1,t) = 0 2 sin(72) + 4 sin(372) at lt=0
d1=8
d2=9
lu for Find the solution u(x,t) for the l-D wave equation-=- Qx2 25 at2 (a) oo < x < oo with initial conditions u(x,0)-A(x) , where A(x) Is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and t, somewhat similar to f(x) on page 85 of the Notes Part 2. d2+5 di+10 di+15dı+20 (b) Check for the wave equation in (a) that if (x...
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