Differential Equations with Boundary-Value Problems
9th Edition
ISBN: 9781337632515
Author: Dennis G. Zill
Publisher: Cengage Learning US
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Textbook Question
Chapter 5.3, Problem 16E
A uniform chain of length L, measured in feet, is held vertically so that the lower end just touches the floor. The chain weighs 2 lb/ft. The upper end that is held is released from rest at t = 0 and the chain falls straight down. If x(t) denotes the length of the chain on the floor at time t, air resistance is ignored, and the positive direction is taken to be downward, then
- (a) Solve for v in terms of x. Solve for x in terms of t. Express v in terms of t.
- (b) Determine how long it takes for the chain to fall completely to the ground.
- (c) What velocity does the model in part (a) predict for the upper end of the chain as it hits the ground?
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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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