PROBLEM 3 Method of lines method combines finite difference method with one dimensional numerical differential solution...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
PROBLEM 3 Method of lines method combines finite difference method with one dimensional numerical differential solution methods (such as Runge-Kutta) to solve partial differentil equations. Method details and an example problem is given below. Now consider the following problem: We are looking to find an expression for the transverse displacement y(xt) of a string streched at t=0 time between the points y(0,0) and y(c.0). The string is initially displaced into position y(x,0) =f(x), and released at rest from that position. It is assumed that no external forces act along the string. String is frictionless. f(x) Then equation of motion of frictionless string will be 82y(x,t) 8t 8y(x, t) 8x Where a = F, is tensile force po is linear density of string (assumed to be constant) So boundary conditions of the equation: 8y(x, t) 8t 0 xc y(x, t) = f(x) at t=0 0xsc apply solution to a specific function: y y(x, t) = 0 atx=0 t> 0 y(x, t) = 0 at x = ct > 0 (1,h) = 0 at t=0 f(x) f(x) = (2,0) Let the string streched between points (0.0) and (2,0) and suppose that its midpoint is raised to a height above the x axis. The string is then released from rest in to a position consisting of two line segments. In this case function f(x) can be described as: 02052/ Lax + 2h PROBLEM 3 Method of lines method combines finite difference method with one dimensional numerical differential solution methods (such as Runge-Kutta) to solve partial differentil equations. Method details and an example problem is given below. Now consider the following problem: We are looking to find an expression for the transverse displacement y(xt) of a string streched at t=0 time between the points y(0,0) and y(c.0). The string is initially displaced into position y(x,0) =f(x), and released at rest from that position. It is assumed that no external forces act along the string. String is frictionless. f(x) Then equation of motion of frictionless string will be 82y(x,t) 8t 8y(x, t) 8x Where a = F, is tensile force po is linear density of string (assumed to be constant) So boundary conditions of the equation: 8y(x, t) 8t 0 xc y(x, t) = f(x) at t=0 0xsc apply solution to a specific function: y y(x, t) = 0 atx=0 t> 0 y(x, t) = 0 at x = ct > 0 (1,h) = 0 at t=0 f(x) f(x) = (2,0) Let the string streched between points (0.0) and (2,0) and suppose that its midpoint is raised to a height above the x axis. The string is then released from rest in to a position consisting of two line segments. In this case function f(x) can be described as: 02052/ Lax + 2h
Expert Answer:
Answer rating: 100% (QA)
The question describes a problem related to the transverse displacement yxt of a string fixed at two ... View the full answer
Related Book For
Numerical Methods With Chemical Engineering Applications
ISBN: 9781107135116
1st Edition
Authors: Kevin D. Dorfman, Prodromos Daoutidis
Posted Date:
Students also viewed these mechanical engineering questions
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
XYZ What is the difference between volatile and nonvolatile memory? Is RAM volatile or nonvolatile? Is ROM volatile or nonvolatile? 7.9 Registers perform a very important role in the fetch-execute...
-
A woman flies from Phoenix to Denver (a distance of 800 mi) at a rate 40 mph faster than on the return trip. If the total time of the trip is 9 hrs, what was her rate going to Denver, and what was...
-
The Asian financial crisis that began in July 1997 wreaked havoc throughout the currency markets of East Asia. a. Which of the following currencies had the largest depreciations or devaluations...
-
To what extent are the SBU strategy and product strategy interrelated?
-
What is the magnetic field at the center of the loop in Figure P24.17? Figure P24.17 2.0 cm 5.0 A
-
You are the division president of Stable Division of Giga-Corp. Your friend, Ligia, is the division president of Giga-Corp.s Turmoil Division. These are the only divisions. Each division has 5,000...
-
2. A projectile is launched into the air. The projectile has a mass of 50 kg and is travelling with a speed of 100 m/s at the peak (as shown in the adjacent figure). a. What is the initial momentum...
-
Carla Company uses the perpetual inventory system. The following information is available for January of the current year, when Carla Company sold 1,600 units of inventory on January 14. Using the...
-
Imagine You were hired as a social worker three months ago at your practicum agency "The International Rescue Committee (IRC)" to community center that provides recreational and well-being programs...
-
Decibee, Inc. has a restricted stock award plan for its employees. It grants 220,000 of its $2.00 par common stock to its selected employees on January 1, 2014 with a vesting period of two years. The...
-
What type of regulation is present in lactose metabolism? What gene regulator is involve in this process? What happens to allow transcription to occur?
-
If the poison arsenate blocks the attachment of phosphate to glyceraldehyde-3-phosphate to produce 3-phosphoglycerate instead of 1,3-bisphosphoglycerate, what would be the impact on the net yield of...
-
Your firm manufactures a generic low-cost product. To be more competitive, you are considering expanding your product line with a new premium version of your product. Below are the details. o Cost of...
-
Date Flounder Company borrowed $38,400 on November 1, 2020, by signing a $38,400, 9%, 3-month note. Prepare Flounder's November 1, 2020, entry; the December 31, 2020, annual adjusting entry; and the...
-
A study conducted by the Toledo police at the intersection of Byrne and Heather downs for the 7 to 9 AM drive time revealed the following number of vehicles that proceeded through the intersection...
-
Consider the setup in Problem 16. Show that the relative speed of the ball and the point of contact on the stick is the same before and immediately after the collision. (This result is analogous to...
-
Answer the following question about this MATLAB function: I get the output x = 0.3333 after one iteration, which is not the correct answer. What is required to fix this code? 1 2 3 4 5 6 7 8 function...
-
To test our claim about the accuracy of these methods, use Program 8.4 to calculate the integral which we know has the value I = 1 for any positive integer m. Program 8.4 We can write a nice compact...
-
Consider the system of ordinary differential equations (a) Confirm that (x,y) = (0,0), (1,1), and (1,1) are steady states of this system. (b) What is the 2 2 steady state Jacobian for this system in...
-
Go to https://www.youtube.com/watch?v=Fp9m4GNwGng to view a brief video on the Brazilian Jet manufacturer Embraer and their use of Critical Chain Project Management for maintenance services. How has...
-
It is sometimes argued that state revenue generated by lotteries is different from tax revenue because people choose to buy lottery tickets. Compare three state revenue sources cigarette excise...
-
Suppose that the demand for personalized license plates and the marginal cost of production in a state is as shown in Figure 16.1. If all the profits go to the government and the state wants to...
Study smarter with the SolutionInn App