1

# A metal rod of length a cm has initial temperature function f(x) = 2 sin 3x...

## Question

###### A metal rod of length a cm has initial temperature function f(x) = 2 sin 3x...

A metal rod of length a cm has initial temperature function f(x) = 2 sin 3x and its two ends are held at temperature zero for all time t>O The heat equation is given as: ди au 4 for 0 < x < it and t > 0 at @x? Boundary conditions: u(0,t) = u(1,t)=0, Initial conditions: u(x,0) = 2 sin 3x By using the method of separation of variables, calculate the general temperature u(x,t) for all cases, k = 22, k = 0, and k = -22.

#### Similar Solved Questions

##### If fifth term of a GP is 2 ,then the product of its 9 terms is ?
If fifth term of a GP is 2 ,then the product of its 9 terms is ?...
##### 125 D. Structure and models of amides Compound Condensed structural formula Instructor's approval for models acetic...
125 D. Structure and models of amides Compound Condensed structural formula Instructor's approval for models acetic acid ammonia acetamide Write the balanced equation for the reaction of acetic acid and ammonia to form acetamide....
##### 1) 2) Evaluate the integrals of the functions graphed by using the formulas for areas of...
1) 2) Evaluate the integrals of the functions graphed by using the formulas for areas of triangles and circles and by subtracting the areas below the x-axis. y 4-x-101 4 3 2 1-x-11 7 10 11 12 13 14" -1 -21 -x+8x- x-12 257 8 + 17 X Use the average of the left-endpoint (L) and right-endpoint ...
##### "based on the given enthalpies, calculate change in H° for the balanced reaction shown" 3. Based...
"based on the given enthalpies, calculate change in H° for the balanced reaction shown" 3. Based on the the hinnad at for given band reaction enthalpics, calculate show o=c=0 H-O-H - H-o- o-o-H c=0 799 KJima HO 463 kalmal cro 358 Kits mol...
##### On January 1, 2015, Lenore, Inc. issued \$800,000, 6% bonds when the market rate was 7%....
On January 1, 2015, Lenore, Inc. issued \$800,000, 6% bonds when the market rate was 7%. Interest is payable semiannually on December 31 and June 30 with bonds maturing on December 31, 2024. The bonds are callable at 103. On December 31, 2018, Lenore retired \$400,000 of the bonds at the call price. A...
##### Prove (X - Y) nZ = (X n 2) - Y
Prove (X - Y) nZ = (X n 2) - Y...
##### A helicopter takes off from a landing at 10:44 am and travels due east at speed...
A helicopter takes off from a landing at 10:44 am and travels due east at speed of 270 km/hr. A second helicopter traveling due south at 180 km/hr towards the pad set to land at 10:56 am/ Determine the rate at which the distance between the helicopters is changing at 10:48 am. (assume the helicopter...
##### Be sure to answer all parts. The following name is incorrect. Draw the structure of the...
Be sure to answer all parts. The following name is incorrect. Draw the structure of the compound and name it correctly. 3-propyl-2-butanone draw structure... (select)...
##### A computer runs a round-robin process scheduler with system contention scope and for a while there...
A computer runs a round-robin process scheduler with system contention scope and for a while there are 4 CPU-intensive processes in the system, without doing any I/O operations. What is the percentage of the CPU utilization allocated to each  process ? Write just the percentage number, wit...
##### The following data from the just completed year are taken from the accounting records of Mason...
The following data from the just completed year are taken from the accounting records of Mason Company: Sales Direct labor cost Raw material purchases Selling expenses Administrative expenses Manufacturing overhead applied to work in process Actual manufacturing overhead costs \$ 660,000 \$ 89,000 \$ 1...
##### Consider the following boundary value problem, r?y" + 19xy' + (81 +2) y = 0, y(1)...
Consider the following boundary value problem, r?y" + 19xy' + (81 +2) y = 0, y(1) = 0, y(e) = 0 (a) Find the eigenvalues. (b) Find the eigenfunctions. Take the arbitrary constant (either cı or c2) from the general solution to be 1....
##### 9.1.67 Solve by completing the square. m2+2m+ 10-0 The solution is m (Simplify your answer. Use...
9.1.67 Solve by completing the square. m2+2m+ 10-0 The solution is m (Simplify your answer. Use a comma to separate answers as needed.)...