In Problems 14-24, you will need a computer and a programmed version of the
Appendix G describes various websites and commercial software that sketch direction fields and automate most of the differential equation algorithms discussed in this book.
In Project C of Chapter 4, it was shown that the simple pendulum equation
has periodic solutions when the initial displacement and velocity are small. Show that the period of the solution may depend on the initial conditions by using the vectorized Runge-Kutta algorithm with
a.
b.
c.
[Hint: Approximate the length of time it takes to reach
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardQuestion 6 Find the real-valued solution to the following IVP: 3 - (13¹) ₁ ý, ÿ (0) = ( ₂ ) Show your work: Show all steps involved in finding the solution to the IVP. I shouldarrow_forwardThis is an electromagnetics problem. Can you please help me to answer this step by step. Thank you so mucharrow_forward
- This problem set deals with the problem of non-constant acceleration. Two researchers from Fly By Night Industries conduct an experiment with a sports car on a test track. While one is driving the car, the other will look at the speedometer and record the speed of the car at one- second intervals. Now, these aren't official researchers and this isn't an official test track, so the speeds are in miles per hour using an analog speedometer. The data set they create is: {(1,5), (2, 2), (3, 30), (4, 50), (5, 65), (6,70)} Z = 25 They notice that the acceleration is not a constant value. They decide that a fourth-degree polynomial will be the best to describe the speed of the car as a function of time. The task here is to determine the fourth-degree polynomial that fits this data set the best. 1. Construct the system of normal equations A¹ AX = A¹b. AT A = A¹b = 2. Solve the system of normal equations. (I don't want you doing this by hand. Use a calculator or app.) x =arrow_forwardThis problem set deals with the problem of non-constant acceleration. Two researchers from Fly By Night Industries conduct an experiment with a sports car on a test track. While one is driving the car, the other will look at the speedometer and record the speed of the car at one- second intervals. Now, these aren't official researchers and this isn't an official test track, so the speeds are in miles per hour using an analog speedometer. The data set they create is: {(1,5), (2, 2), (3, 30), (4, 50), (5, 65), (6,70)} Z = 25 They notice that the acceleration is not a constant value. They decide that a fourth-degree polynomial will be the best to describe the speed of the car as a function of time. The task here is to determine the fourth-degree polynomial that fits this data set the best. 1. Construct the system of normal equations A¹ Ax = A¹b. AT A = АТЬ= 2. Solve the system of normal equations. (I don't want you doing this by hand. Use a calculator or app.) x =arrow_forwardThis problem set deals with the problem of non-constant acceleration. Two researchers from Fly By Night Industries conduct an experiment with a sports car on a test track. While one is driving the car, the other will look at the speedometer and record the speed of the car at one- second intervals. Now, these aren't official researchers and this isn't an official test track, so the speeds are in miles per hour using an analog speedometer. The data set they create is: {(1,5), (2, z), (3, 30), (4, 50), (5, 65), (6, 70)} Z = 25 They notice that the acceleration is not a constant value. They decide that a fourth-degree polynomial will be the best to describe the speed of the car as a function of time. The task here is to determine the fourth-degree polynomial that fits this data set the best. 1. Use a general fourth-degree polynomial and Fly By Night's data to construct six equations. Note that the equations are linear in the coefficients. Write the equations here: 2. Construct the…arrow_forward
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