Introductory Mathematics for Engineering Applications

1st Edition

ISBN: 9781118141809

Author: Nathan Klingbeil

Publisher: WILEY

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Textbook Question

Chapter 10, Problem 27P

Repeat problem P10-26 if the displacement y ( t ) of a spring-mass (m=500 gm and k=5 N/m) system shown is given by 0.5 y ¯ ( t ) + 5 y ( t ) = 0 and y ( 0 ) = 10 c m .

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Chapter 10, Problem 26P

Chapter 10, Problem 28P

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2. Consider the ODE u' = ƒ (u) = u² + r where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r: (a) Sketch ƒ(u) = u² + r and determine the equilibrium points. (b) Draw the phase line. (d) Determine the stability of the equilibrium points. (d) Plot the direction field and some sample solutions,i.e., u(t) (e) Describe how location of the equilibrium points and their stability change as you increase the parameter r. (f) Using the matlab program phaseline.m generate a solution for each value of r and the initial condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption. (g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to turn in a plot for (g), just describe what happens.

True or False and why

10 5 Obtain by multiplying matrices the composite coordinate transformation of two transformations, first x' = (x + y√√2+2)/2 y' = z' (x√√2-2√2)/2 z = (-x+y√√2-2)/2 followed by x" = (x'√√2+z'√√2)/2 y" = (-x'y'√√2+2')/2 z" = (x'y'√√2-2')/2.

Chapter 10 Solutions

Introductory Mathematics for Engineering Applications

Ch. 10 - A faucet supplies fluid to a container of...Ch. 10 - The initial temperature of the hot coffee cup...Ch. 10 - A constant voltage vs(t)=10V is applied to the RC...Ch. 10 - Repeat parts (a)-(d) of the problem P10-3 if R=10k...Ch. 10 - Repeat parts (a)-(d) of the problem P10-3 if R=20k...Ch. 10 - A constant voltage vs(t)=10V is applied to the RC...Ch. 10 - Repeat problems P10-6 if R=200k and C=100F.Ch. 10 - Repeat problems P10-6 if R=100k, C=50F, vs(t)=20V...Ch. 10 - A sinusoidal voltage vs(t)=10sin(0.01t)V is...Ch. 10 - Repeat problem P10-9 if R=10k and C=10F.

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