Differential Equations with Boundary-Value Problems
9th Edition
ISBN: 9781337632515
Author: Dennis G. Zill
Publisher: Cengage Learning US
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 5.1, Problem 23E
Spring/Mass Systems: Free Damped Motion
In Problems 21–24 the given figure represents the graph of an equation of motion for a damped spring/mass system. Use the graph to determine
- (a) whether the initial displacement is above or below the equilibrium position and
- (b) whether the mass is initially released from rest, heading downward, or heading upward.
Figure 5.1.19 Graph for Problem 22
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Please solving problem2
Problem1
We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. (This model is the same as in Prob. 1 of HW#2).We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.
Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.
This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one.
A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The
wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture.
A
B
A
B
at some instant, the piston will be tangent to the circle
(a) Express the x and y coordinates of point A as functions of t:
x= 2 cos(3πt)
and y= 2 sin(3t)
(b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds:
-cot(3πt)
sin(3лt)
(c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411-
4
-2 sin (3лt)
(d)…
Chapter 5 Solutions
Differential Equations with Boundary-Value Problems
Ch. 5.1 - 5.1.1 Spring/Mass systems: Free Undamped Motion A...Ch. 5.1 - Spring/Mass Systems: Free Undamped Motion A...Ch. 5.1 - Spring/Mass Systems: Free Undamped Motion A mass...Ch. 5.1 - Spring/Mass Systems: Free Undamped Motion...Ch. 5.1 - Spring/Mass Systems: Free Undamped Motion A mass...Ch. 5.1 - Spring/Mass Systems: Free Undamped Motion A force...Ch. 5.1 - Prob. 7ECh. 5.1 - Spring/Mass Systems: Free Undamped Motion A mass...Ch. 5.1 - Prob. 9ECh. 5.1 - 5.1.1Spring/Mass Systems: Free Undamped Motion A...
Ch. 5.1 - A mass weighing 64 pounds stretches a spring 0.32...Ch. 5.1 - A mass of 1 slug is suspended from a spring whose...Ch. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Spring/Mass Systems: Free Undamped Motion A model...Ch. 5.1 - Prob. 20ECh. 5.1 - 5.1.2 Spring/Mass systems: Free Damped Motion In...Ch. 5.1 - Spring/Mass Systems: Free Damped Motion In...Ch. 5.1 - Spring/Mass Systems: Free Damped Motion In...Ch. 5.1 - Prob. 24ECh. 5.1 - Spring/Mass System: Free Damped Motion A mass...Ch. 5.1 - Spring/Mass Systems: Free Damped Motion A 4-foot...Ch. 5.1 - A 1-kilogram mass is attached to a spring whose...Ch. 5.1 - Prob. 28ECh. 5.1 - Spring/Mass Systems: Free Damped Motion A force of...Ch. 5.1 - After a mass weighing 10 pounds is attached to a...Ch. 5.1 - Spring/Mass Systems: Free Damped Motion A mass...Ch. 5.1 - f(t)=cos5t+sin2tCh. 5.1 - Spring/Mass Systems: Free Damped Motion A mass...Ch. 5.1 - A mass of 1 slug is attached to a spring whose...Ch. 5.1 - Prob. 35ECh. 5.1 - In Problem 35 determine the equation of motion if...Ch. 5.1 - Spring/Mass Systems: Driven Motion When a mass of...Ch. 5.1 - Spring/Mass Systems: Driven Motion In Problem 37...Ch. 5.1 - Spring/Mass Systems: Driven Motion A mass m is...Ch. 5.1 - A mass of 100 grams is attached to a spring whose...Ch. 5.1 - Spring/Mass Systems: Driven Motion In Problems 41...Ch. 5.1 - In Problems 41 and 42 solve the given...Ch. 5.1 - Series Circuit Analogue (a) Show that the solution...Ch. 5.1 - Compare the result obtained in part (b) of Problem...Ch. 5.1 - (a) Show that x(t) given in part (a) of Problem 43...Ch. 5.1 - Series Circuit Analogue Find the charge on the...Ch. 5.1 - Series Circuit Analogue Find the charge on the...Ch. 5.1 - Series Circuit Analogue In Problems 51 and 52 find...Ch. 5.1 - In Problems 51 and 52 find the charge on the...Ch. 5.1 - Prob. 53ECh. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - Find the steady-state current in an LRC-series...Ch. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Series Circuit Analogue Find the charge on the...Ch. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.2 - (a) The beam is embedded at its left end and free...Ch. 5.2 - (a) The beam is simply supported at both ends, and...Ch. 5.2 - (a) The beam is embedded at its left end and...Ch. 5.2 - (a) The beam is embedded at its left end and...Ch. 5.2 - Prob. 6ECh. 5.2 - A cantilever beam of length L is embedded at its...Ch. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 - In Problems 920 find the eigenvalues and...Ch. 5.2 - In Problems 920 find the eigenvalues and...Ch. 5.2 - In Problems 920 find the eigenvalues and...Ch. 5.2 - Prob. 13ECh. 5.2 - In Problems 920 find the eigenvalues and...Ch. 5.2 - In Problems 920 find the eigenvalues and...Ch. 5.2 - Prob. 16ECh. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - Eigenvalues and Eigenfunctions In Problems 920...Ch. 5.2 - Eigenvalues and Eigenfunctions In Problems 920...Ch. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Prob. 23ECh. 5.2 - The critical loads of thin columns depend on the...Ch. 5.2 - Prob. 25ECh. 5.2 - Rotating String Consider the boundary-value...Ch. 5.2 - Prob. 28ECh. 5.2 - Additional Boundary-Value Problems Temperature in...Ch. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.2 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 - Damped Motion Assume that the model for the...Ch. 5.2 - Additional Boundary-Value Problems y + 16y = 0,...Ch. 5.2 - Additional Boundary-Value Problems y + 16y = 0,...Ch. 5.2 - Consider the boundary-value problem...Ch. 5.2 - Show that the eigenvalues and eigenfunctions of...Ch. 5.3 - Find a linearization of the differential equation...Ch. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - A uniform chain of length L, measured in feet, is...Ch. 5.3 - Pursuit curve In a naval exercise a ship S1 is...Ch. 5.3 - Pursuit curve In another naval exercise a...Ch. 5.3 - Prob. 19ECh. 5.3 - Prob. 21ECh. 5 - If a mass weighing 10 pounds stretches a spring...Ch. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - Pure resonance cannot take place in the presence...Ch. 5 - Prob. 5RECh. 5 - Prob. 6RECh. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Prob. 9RECh. 5 - Prob. 10RECh. 5 - Prob. 11RECh. 5 - Prob. 12RECh. 5 - Prob. 13RECh. 5 - Prob. 14RECh. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - A mass weighing 4 pounds stretches a spring 18...Ch. 5 - Find a particular solution for x + 2x + 2x = A,...Ch. 5 - Prob. 19RECh. 5 - (a) A mass weighing W pounds stretches a spring 12...Ch. 5 - A series circuit contains an inductance of L= 1 h,...Ch. 5 - Prob. 22RECh. 5 - Consider the boundary-value problem...Ch. 5 - Prob. 25RECh. 5 - Prob. 26RECh. 5 - Suppose the mass m in the spring/mass system in...Ch. 5 - Prob. 28RECh. 5 - Prob. 29RECh. 5 - Spring pendulum The rotational form of Newtons...Ch. 5 - Prob. 31RECh. 5 - Galloping Gertie Bridges are good examples of...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- 5. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.AE.003. y y= ex² 0 Video Example x EXAMPLE 3 (a) Use the Midpoint Rule with n = 10 to approximate the integral कर L'ex² dx. (b) Give an upper bound for the error involved in this approximation. SOLUTION 8+2 1 L'ex² d (a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.) dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)] 0.1 [0.0025 +0.0225 + + e0.0625 + 0.1225 e0.3025 + e0.4225 + e0.2025 + + e0.5625 €0.7225 +0.9025] The figure illustrates this approximation. (b) Since f(x) = ex², we have f'(x) = 0 ≤ f'(x) = < 6e. ASK YOUR TEACHER and f'(x) = Also, since 0 ≤ x ≤ 1 we have x² ≤ and so Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final answer to five decimal places.) 6e(1)3 e 24( = ≈arrow_forward1. Consider the following preference ballots: Number of voters Rankings 6 5 4 2 1st choice A DCB DC 2nd choice B B D 3rd choice DCBD 4th choice CA AAA For each of the four voting systems we have studied, determine who would win the election in each case. (Remember: For plurality with runoff, all but the top two vote-getters are simultaneously eliminated at the end of round 1.)arrow_forwardPractice k Help ises A 96 Anewer The probability that you get a sum of at least 10 is Determine the number of ways that the specified event can occur when two number cubes are rolled. 1. Getting a sum of 9 or 10 3. Getting a sum less than 5 2. Getting a sum of 6 or 7 4. Getting a sum that is odd Tell whether you would use the addition principle or the multiplication principle to determine the total number of possible outcomes for the situation described. 5. Rolling three number cubes 6. Getting a sum of 10 or 12 after rolling three number cubes A set of playing cards contains four groups of cards designated by color (black, red, yellow, and green) with cards numbered from 1 to 14 in each group. Determine the number of ways that the specified event can occur when a card is drawn from the set. 7. Drawing a 13 or 14 9. Drawing a number less than 4 8. Drawing a yellow or green card 10. Drawing a black, red, or green car The spinner is divided into equal parts. Find the specified…arrow_forward
- Problem 1.We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.(d) We assume that you sell the American put to a market participant A for the pricefound in (b). Explain how you act on the market…arrow_forwardWhat is the standard scores associated to the left of z is 0.1446arrow_forward2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.015. Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) ASK YOUR TEACHER 3 1 3 + dy, n = 6 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule Need Help? Read It Watch Itarrow_forward
- This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3πt) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot (3πt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +41/1 (d) Express the slope of the rod…arrow_forwardConsider the proof below: Proposition: If m is an even integer, then 5m +4 is an even integer. Proof: We see that |5m+4=10n+4 = 2(5n+2). Therefore, 5m+4 is an even integer. **Note: you may assume the proof is valid, just poorly written. Based upon the Section 1.3 screencast and the reading assignment, select all writing guidelines that are missing in the proof. Proof begins by stating assumptions ✓ Proof has an invitational tone/uses collective pronouns Proof is written in complete sentences Each step is justified ☐ Proof has a clear conclusionarrow_forwardNote: The purpose of this problem below is to use computational techniques (Excelspreadsheet, Matlab, R, Python, etc.) and code the dynamic programming ideas seen inclass. Please provide the numerical answer to the questions as well as a sample of yourwork (spreadsheet, code file, etc.).We consider an N-period binomial model with the following properties: N = 60, thecurrent stock price is S0 = 1000; on each period, the stock price increases by 0.5% whenit moves up and decreases by 0.3% when it moves down. The annual interest rate on themoney market is 5%. (Notice that this model is a CRR model, which means that thebinomial tree is recombining.)(a) Find the price at time t0 = 0 of a (European) call option with strike price K = 1040and maturity T = 1 year.(b) Find the price at time t0 = 0 of a (European) put option with strike price K = 1040and maturity T = 1 year.(c) We consider now, that you are at time t5 (i.e. after 5 periods, which represents 1month later). Assume that the stock…arrow_forward
- 4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.024. Find the approximations Tη, Mn, and S, to the integral computer algebra system.) ASK YOUR TEACHER PRACTICE ANOTHER 4 39 √ dx for n = 6 and 12. Then compute the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. You may wish to use the sum command on a n Tn Mn Sp 6 12 n ET EM Es 6 12 What observations can you make? In particular, what happens to the errors when n is doubled? As n is doubled, ET and EM are decreased by a factor of about Need Help? Read It ' and Es is decreased by a factor of aboutarrow_forward6. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.001. ASK YOUR TEACHER PRACTICE ANOTHER Let I = 4 f(x) dx, where f is the function whose graph is shown. = √ ² F(x 12 4 y f 1 2 (a) Use the graph to find L2, R2 and M2. 42 = R₂ = M₂ = 1 x 3 4arrow_forwardThe general solution X'=Ax is given. Discuss the nature of the solutions in a neighborhood of (0,0) -2-2 (²) |a) A = (23) X(A) = (₁ (fi)e* + (2 (2) eht -2-5arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSON
Discrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
Trigonometry - Harmonic Motion - Equation Setup; Author: David Hays;https://www.youtube.com/watch?v=BPrZnn3DJ6Q;License: Standard YouTube License, CC-BY
Simple Harmonic Motion - An introduction : ExamSolutions Maths Revision; Author: ExamSolutions;https://www.youtube.com/watch?v=tH2vldyP5OE;License: Standard YouTube License, CC-BY