Differential Equations with Boundary-Value Problems
9th Edition
ISBN: 9781337632515
Author: Dennis G. Zill
Publisher: Cengage Learning US
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Chapter 5.3, Problem 15E
(a)
To determine
The length of the chain intuitively to be lifted up with a constant
(b)
To determine
The initial velocity of the chain which is lifted up with a constant
(c)
To determine
The interval for
(d)
To determine
The reason for periodic nature of the solution
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Consider 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
=
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**Note: you may assume the proof is valid, just poorly written.
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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
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Read It
'
and Es is decreased by a factor of about
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...
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