5

# (20 points) A function u(z,t) satisfies the PDEUII0 <I < 2 t20and the homogeneous boundary conditionsu(0,t) =0,2(2,+) = 0,t20Setting u(z,t) F(r)G(t) implies t...

## Question

###### (20 points) A function u(z,t) satisfies the PDEUII0 <I < 2 t20and the homogeneous boundary conditionsu(0,t) =0,2(2,+) = 0,t20Setting u(z,t) F(r)G(t) implies the separated equations F" 2F" AF = 0 and G' + AG = 0_ where is a separation constant _(a) Find all real eigenvalues A and corresponding eigenfunctions F(z) of the eigenvalue problem con sisting of the separated equation for F(r) and the boundary conditions F (0) and F(2) implied by the homogeneous BCs for u(I,t) (Hi

(20 points) A function u(z,t) satisfies the PDE UII 0 <I < 2 t20 and the homogeneous boundary conditions u(0,t) =0, 2(2,+) = 0, t20 Setting u(z,t) F(r)G(t) implies the separated equations F" 2F" AF = 0 and G' + AG = 0_ where is a separation constant _ (a) Find all real eigenvalues A and corresponding eigenfunctions F(z) of the eigenvalue problem con sisting of the separated equation for F(r) and the boundary conditions F (0) and F(2) implied by the homogeneous BCs for u(I,t) (Hint: Iyou need only consider Solve the separated equation for G(t) with the values for obtained in part (a), and then SUm over all of the product solutions F(r)G(t) found to form the general solution satisfying the PDE and its BCs. Find the solution of the PDE and BCs subject to the initial condition u(z,0) = 3ef sin(Tr) 2u:

#### Similar Solved Questions

##### Use the Runge-Kutta methoc witn step sizes XV 2v = 8x2 v (2) =5 at x= ]0.1_ to find approximate values of tne solution cfAnd compare tnis approximate value with the values cfthe exact sclution 12 v=2x2
Use the Runge-Kutta methoc witn step sizes XV 2v = 8x2 v (2) =5 at x= ] 0.1_ to find approximate values of tne solution cf And compare tnis approximate value with the values cfthe exact sclution 12 v=2x2...
##### Determine ifthe vector field F is conservative: Ifit is find a potential function for the vector field F(x,J,z) = 6+y2+7.1)
Determine ifthe vector field F is conservative: Ifit is find a potential function for the vector field F(x,J,z) = 6+y2+7.1)...
##### "fR ISTJClQuestion 21How many moles of gas are present in a balloon that measures 1.29 Lon a summer day when the atmospheric pressure is 0.992atm and the temperature is 35 %C?HTML EditorpB [ 4 4 A I 8 D3 3XT 12ptParagraph
"fR ISTJCl Question 21 How many moles of gas are present in a balloon that measures 1.29 Lon a summer day when the atmospheric pressure is 0.992atm and the temperature is 35 %C? HTML Editorp B [ 4 4 A I 8 D 3 3 X T 12pt Paragraph...
##### Findthe probability thatfallsin the shaded area_A.0.525B. 0.438C.0.1257D.0.0729
Findthe probability that fallsin the shaded area_ A.0.525 B. 0.438 C.0.1257 D.0.0729...
##### Fig: 4.2 Cross-section of an iron cylinder with copper wires wound around the cylinder, here with n = 8 windings_ The inner circles are cross-sections of the copper wire coming up ("north" and the outer circles are cross-sections of the copper wire going down into the plane south")
Fig: 4.2 Cross-section of an iron cylinder with copper wires wound around the cylinder, here with n = 8 windings_ The inner circles are cross-sections of the copper wire coming up ("north" and the outer circles are cross-sections of the copper wire going down into the plane south")...
##### Minulcs Due Sun 06/21/2020 11459Find an Euler Path for the pTph Enicrvour Tesnonse I0t cxamnic ABCDEA.Mluencventices thc order thcy arc Vislted,Lntcr tcrt ImereatGet help; Vidco]Pcints cossidle: Unlimited attempts scone last attempt;Ecdnegradebook:[email protected]?ox:
Minulcs Due Sun 06/21/2020 11459 Find an Euler Path for the pTph Enicrvour Tesnonse I0t cxamnic ABCDEA. Mluenc ventices thc order thcy arc Vislted, Lntcr tcrt Imereat Get help; Vidco] Pcints cossidle: Unlimited attempts scone last attempt; Ecdne gradebook: 5kmit To0 @W?ox:...
##### Convert 152564, which is a base-10 number, to Mayan notation: When you are done, choose the symbol that should be placed in the row that corresponds to the 2O's place in the Mayan number. Make your choice from the selections below_ 76"
Convert 152564, which is a base-10 number, to Mayan notation: When you are done, choose the symbol that should be placed in the row that corresponds to the 2O's place in the Mayan number. Make your choice from the selections below_ 76"...
##### The locus of point of intersection of tangents at the end of normal chord of hyperbola $x^{2}-y^{2}=a^{2}$ is(A) $a^{2}left(y^{2}-x^{2}ight)=4 x^{2} y^{2}$(B) $a^{2}left(y^{2}+x^{2}ight)=4 x^{2} y^{2}$(C) $y^{2}+x^{2}=4 a^{2} x^{2}$(C) none of these
The locus of point of intersection of tangents at the end of normal chord of hyperbola $x^{2}-y^{2}=a^{2}$ is (A) $a^{2}left(y^{2}-x^{2} ight)=4 x^{2} y^{2}$ (B) $a^{2}left(y^{2}+x^{2} ight)=4 x^{2} y^{2}$ (C) $y^{2}+x^{2}=4 a^{2} x^{2}$ (C) none of these...
##### OeitanIscnonbiJet O al"aa4Ln"FMCUDUL rd Wocrd J Jwmn dimncit unislcurv tn N7 Whaiooxuim "puteritul t nolnt lero? aaba Czeiclu& (Q,047IIn thnt @xudlin Ite Rol ~wth JccthloleJen
Oeitan Iscnonbi Jet O al"aa 4Ln" FMCUDUL rd Wocrd J Jwmn dimncit unislcurv tn N7 Whaiooxuim "puteritul t nolnt lero? aaba Czeiclu& (Q,047IIn thnt @xudlin Ite Rol ~wth Jccthlole Jen...
##### You are handed bufier solution of unknown composition that you know contalns equal concentratlons ofa weak acid andIG conjugate base, Which of the following statements about the pH ofthe buffer iS most accurate?Selertan answer and submit For KGybourd navizeticn,uY vpidoxn#cyetosclcct n anwicrPH = 7.0,because there equal concentrations of acld and base In the buffer and otheracid and base neutralize eachbecause bufiers are always madeup of an acid and its conjugate 02s8, the solution Is- (wrays
You are handed bufier solution of unknown composition that you know contalns equal concentratlons ofa weak acid andIG conjugate base, Which of the following statements about the pH ofthe buffer iS most accurate? Selertan answer and submit For KGybourd navizeticn,uY vpidoxn #cyetosclcct n anwicr PH ...
##### 1Spts . 3B. Write detailed mechanism including all resonance structures for the following Hoffman degradation. (Hint: clearly show the isocyanate intermediate)NHzBrz 4NaOHNHz2H,0 2NaBr NazCOzHzO
1Spts . 3B. Write detailed mechanism including all resonance structures for the following Hoffman degradation. (Hint: clearly show the isocyanate intermediate) NHz Brz 4NaOH NHz 2H,0 2NaBr NazCOz HzO...
##### Solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. $\left\{\begin{array}{l}x+2 y=-7 \\ x+y=-3\end{array}\right.$
Solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. $\left\{\begin{array}{l}x+2 y=-7 \\ x+y=-3\end{array}\right.$...
##### Box of mass m is in equilibrium on a rough surface, The coefficient of static friction between the box ad the surface on which it rests iS /. The box is subject to a force 0f magnitude Ti which i5 directed at a angle 01 ad another force of magnitude Tz which is directed at angle Oz as shown in the figure:@Assume that Ti =37.8N, 01 = 26.3 degrees, T; = 22.0N, and 0, 30.3 degrees For what mass I5 the normal force on the box exactly ON? Answer in kg_Answer:Save response
box of mass m is in equilibrium on a rough surface, The coefficient of static friction between the box ad the surface on which it rests iS /. The box is subject to a force 0f magnitude Ti which i5 directed at a angle 01 ad another force of magnitude Tz which is directed at angle Oz as shown in the f...
##### 1)Police estimate that 10% of drivers drive without their seatbelts. If they stop 8 drivers at random,a) What is the probability that exactly two of the 8 drivers aredriving without their seat belts?b) What is the probability that at most two of the 8 drivers aredriving without their seat belts?c) What is the probability that at least three of the 8 drivers aredriving without their seat belts?
1)Police estimate that 10% of drivers drive without their seat belts. If they stop 8 drivers at random, a) What is the probability that exactly two of the 8 drivers are driving without their seat belts? b) What is the probability that at most two of the 8 drivers are driving without their seat belts...
##### Saule Example 2 Ignoting boundarv conditions show equation %4 gu" that the CN FDM 0 0r1 unconditionally stable rendering of the 1D heat
saule Example 2 Ignoting boundarv conditions show equation %4 gu" that the CN FDM 0 0r1 unconditionally stable rendering of the 1D heat...