Homework Answers
Add Answer to:
1. Complete the example started in class: u(r, t) is the solution of the 3 dimensional wave equat...
(3) Solve the following BVP for the Wave Equation using the Fourier Series solution formulac (3a2 u(r, t) 0 u(0, t)0 u(...
(3) Solve the following BVP for the Wave Equation using the Fourier Series solution formulac (3a2 u(r, t) 0 u(0, t)0 u(T, t) 0 u(r, 0) sin(x)2sin(4r) 3sin(8r) (r, 0) 10sin(2x)20sin (3r)- 30sin (5r) (r, t) E (0, ) x (0, 0o) t >0 t > 0 1
(3) Solve the following BVP for the Wave Equation using the Fourier Series solution formulac (3a2 u(r, t) 0 u(0, t)0 u(T, t) 0 u(r, 0) sin(x)2sin(4r) 3sin(8r) (r, 0) 10sin(2x)20sin (3r)-...
3. Find the solution to the two-dimensional heat equation, ut = u -oo < ! < oo,-oo < y < oo) with...
3. Find the solution to the two-dimensional heat equation, ut = u -oo < ! < oo,-oo < y < oo) with initial data u(z,y, 0) = re- + uw İn the r-y plane (that is,
3. Find the solution to the two-dimensional heat equation, ut = u -oo
(2) Solve the following BVP for the Wave Equation using the Fourier Serics solution formulac (42- u(r, t)= 0 u(0, t) 0...
(2) Solve the following BVP for the Wave Equation using the Fourier Serics solution formulac (42- u(r, t)= 0 u(0, t) 0 u(5, t) 0 u(r, 0) sin(T) 12sin(T) ut(r, 0)0 (r, t) E (0,5) x (0, oo) t > 0 t > 0
(2) Solve the following BVP for the Wave Equation using the Fourier Serics solution formulac (42- u(r, t)= 0 u(0, t) 0 u(5, t) 0 u(r, 0) sin(T) 12sin(T) ut(r, 0)0 (r, t) E (0,5) x...
1. Let u be a solution of the wave equation u 0. Let the points A, B, C, D be the vertices of the...
1. Let u be a solution of the wave equation u 0. Let the points A, B, C, D be the vertices of the paralleogram formed by the two pairs of characteristic lines r-ctC1,x- ct-2,+ ct- di,r +ct- d2 Show that u (A)+u (C)-u (B) + u (D Use this to find u satisfying For which (x, t) can you determine u (x, t) uniquely this way? 2. Suppose u satisfies the wave equation utt -curr0 in the strip 0...
Let u be the solution to the initial boundary value problem for the Heat Equation an(t,r)-301a(t, z), te(0,00), z E (0,3); with initial condition 3 0 and with boundary conditions 6xu(t,0)-0, u(t, 3)...
Let u be the solution to the initial boundary value problem for the Heat Equation an(t,r)-301a(t, z), te(0,00), z E (0,3); with initial condition 3 0 and with boundary conditions 6xu(t,0)-0, u(t, 3) 0 Find the solution u using the expansion with the normalization conditions vn (0)-1, wn(0) 1 a. (3/10) Find the functionsw with index n1 b. (3/10) Find the functions vn with index n1 Un c. (4/10) Find the coefficients cn, with index n 1
Let u be...
r Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x, 0)-f(x) and (x,0) (t) r Extra Credit: Write a complete...
r Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x, 0)-f(x) and (x,0) (t)
r Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x, 0)-f(x) and (x,0) (t)
Consider a particle of mass m in an infinite spherical potential well of radius a For write down the energies and corresponding eigen functions ψ--(r,0.9). (3 pt) a) ne that at t-o the wave fu...
Consider a particle of mass m in an infinite spherical potential well of radius a For write down the energies and corresponding eigen functions ψ--(r,0.9). (3 pt) a) ne that at t-o the wave function is given by o)-A. Find the normalization constant A function in this basis. Solve for the coeffici You may find useful the integrals in the front of the (6 pt) d) Now consider the finite potential spherical well with V(r)- ing only the radial part...
3. [4] The solution of the wave equation02, which satisfies the boundary conditions u(0,t) = u(2,...
3. [4] The solution of the wave equation02, which satisfies the boundary conditions u(0,t) = u(2,t) 0, is given by a cos+b sin If u(, t) satisfies the initial conditions u(x, 0)-0 and u(x,0)3sin(Tx) - sin(3T), find the coefficients an and bn Solution: b2 = , bs =- π 97T bn-0 otherwise, and an - 0 for all n 21.
3. [4] The solution of the wave equation02, which satisfies the boundary conditions u(0,t) = u(2,t) 0, is given by...
Question 1: The separated solutions of the o fom u(x.t) -X(x)T(t), with the following solutions: ne-dimensional he...
Question 1: The separated solutions of the o fom u(x.t) -X(x)T(t), with the following solutions: ne-dimensional heat equation dtt lu solutions of are - X(x)-Ax +B and T(t) E X(x) = A cos kx + B sin kx and T(t)=Ee-Det The boundary conditions for a metal rod insulated from both sides arex aum = 0 when x =0, and dx (e) Using the boundary conditions for u(x.t) wrie the boundary conditions for XCx), explain for full marks. (b) Find the...
Consider the initial value problem for the one-dimensional wave equation Write as clear as Ou Ou...
Consider the initial value problem for the one-dimensional wave equation Write as clear as Ou Ou ot (4) possible , some work has been hard to follow Thanks! a(z,0) = e-r2 (a) Determine the solution u(r,t) of (4) (b) Sketch the solution in the xu-plane at t = 0, t = 1 , and (c) Which direction does the wave travel? 2
(3) Solve the following BVP for the Wave Equation using the Fourier Series solution formulac (3a2 u(r, t) 0 u(0, t)0 u(T, t) 0 u(r, 0) sin(x)2sin(4r) 3sin(8r) (r, 0) 10sin(2x)20sin (3r)- 30sin (5r) (r, t) E (0, ) x (0, 0o) t >0 t > 0 1
(3) Solve the following BVP for the Wave Equation using the Fourier Series solution formulac (3a2 u(r, t) 0 u(0, t)0 u(T, t) 0 u(r, 0) sin(x)2sin(4r) 3sin(8r) (r, 0) 10sin(2x)20sin (3r)-...
3. Find the solution to the two-dimensional heat equation, ut = u -oo < ! < oo,-oo < y < oo) with initial data u(z,y, 0) = re- + uw İn the r-y plane (that is,
3. Find the solution to the two-dimensional heat equation, ut = u -oo
(2) Solve the following BVP for the Wave Equation using the Fourier Serics solution formulac (42- u(r, t)= 0 u(0, t) 0 u(5, t) 0 u(r, 0) sin(T) 12sin(T) ut(r, 0)0 (r, t) E (0,5) x (0, oo) t > 0 t > 0
(2) Solve the following BVP for the Wave Equation using the Fourier Serics solution formulac (42- u(r, t)= 0 u(0, t) 0 u(5, t) 0 u(r, 0) sin(T) 12sin(T) ut(r, 0)0 (r, t) E (0,5) x...
1. Let u be a solution of the wave equation u 0. Let the points A, B, C, D be the vertices of the paralleogram formed by the two pairs of characteristic lines r-ctC1,x- ct-2,+ ct- di,r +ct- d2 Show that u (A)+u (C)-u (B) + u (D Use this to find u satisfying For which (x, t) can you determine u (x, t) uniquely this way? 2. Suppose u satisfies the wave equation utt -curr0 in the strip 0...
Let u be the solution to the initial boundary value problem for the Heat Equation an(t,r)-301a(t, z), te(0,00), z E (0,3); with initial condition 3 0 and with boundary conditions 6xu(t,0)-0, u(t, 3) 0 Find the solution u using the expansion with the normalization conditions vn (0)-1, wn(0) 1 a. (3/10) Find the functionsw with index n1 b. (3/10) Find the functions vn with index n1 Un c. (4/10) Find the coefficients cn, with index n 1
Let u be...
r Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x, 0)-f(x) and (x,0) (t)
r Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x, 0)-f(x) and (x,0) (t)
Consider a particle of mass m in an infinite spherical potential well of radius a For write down the energies and corresponding eigen functions ψ--(r,0.9). (3 pt) a) ne that at t-o the wave function is given by o)-A. Find the normalization constant A function in this basis. Solve for the coeffici You may find useful the integrals in the front of the (6 pt) d) Now consider the finite potential spherical well with V(r)- ing only the radial part...
3. [4] The solution of the wave equation02, which satisfies the boundary conditions u(0,t) = u(2,t) 0, is given by a cos+b sin If u(, t) satisfies the initial conditions u(x, 0)-0 and u(x,0)3sin(Tx) - sin(3T), find the coefficients an and bn Solution: b2 = , bs =- π 97T bn-0 otherwise, and an - 0 for all n 21.
3. [4] The solution of the wave equation02, which satisfies the boundary conditions u(0,t) = u(2,t) 0, is given by...
Question 1: The separated solutions of the o fom u(x.t) -X(x)T(t), with the following solutions: ne-dimensional heat equation dtt lu solutions of are - X(x)-Ax +B and T(t) E X(x) = A cos kx + B sin kx and T(t)=Ee-Det The boundary conditions for a metal rod insulated from both sides arex aum = 0 when x =0, and dx (e) Using the boundary conditions for u(x.t) wrie the boundary conditions for XCx), explain for full marks. (b) Find the...
Consider the initial value problem for the one-dimensional wave equation Write as clear as Ou Ou ot (4) possible , some work has been hard to follow Thanks! a(z,0) = e-r2 (a) Determine the solution u(r,t) of (4) (b) Sketch the solution in the xu-plane at t = 0, t = 1 , and (c) Which direction does the wave travel? 2
Most questions answered within 3 hours.
-
4. Atom hybridization changes in many chemical reactions. In
each of the following reactions, determine what...
asked 2 minutes ago -
1) Action potential
a) Explain how an action potential moves down a cell wall. Be
very...
asked 4 minutes ago -
Suppose you fell into an accretion disc that swept you into a
supermassive black hole. On...
asked 9 minutes ago -
An automobile travels on a straight road for 40 km at 45 km/h.
It then continues...
asked 17 minutes ago -
1)
A student sitting on a chair on a circular platform of
negligible mass rotates freely...
asked 29 minutes ago -
Bird Enterprises has no debt. Its current total value is $47.2
million. Assume the company sells...
asked 32 minutes ago -
5. What is span of control? List three factors that may affect
span of control.
6....
asked 36 minutes ago -
How can you visualize anthranilic acid on TLC plates? How can
you visualize carboxylic acids on...
asked 35 minutes ago -
Scenario:
Anytown FD is a combination department with one station. Its
district is surrounded by four...
asked 48 minutes ago -
5. Ethics deals with the moral quality, fitness, or propriety of
a course of action that...
asked 49 minutes ago -
Single Plantwide Factory Overhead Rate
Kennedy Appliance Inc.’s Machining Department incurred $102,900
of factory overhead cost...
asked 51 minutes ago -
Two particles with charges +4e and -7e are
initially very far apart (effectively an infinite distance...
asked 1 hour ago