MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS
8th Edition
ISBN: 9780357537343
Author: Johnson
Publisher: CENGAGE L
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Chapter 11.2, Problem 17E
To determine
To Find:
The information required for a market analyst to predict the future market share of a product and the process for obtaining such information.
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- Suppose that you have the differential equation:
dy
= (y - 2) (y+3)
dx
a. What are the equilibrium solutions for the differential equation?
b. Where is the differential equation increasing or decreasing? Show how you know.
Showing them on the drawing is not enough.
c. Where are the changes in concavity for the differential equation? Show how you
know. Showing them on the drawing is not enough.
d. Consider the slope field for the differential equation. Draw solution curves given the
following initial conditions:
i. y(0) = -5
ii. y(0) = -1
iii. y(0) = 2
5. Suppose that a mass of 5 stretches a spring 10. The mass is acted on by an external force
of F(t)=10 sin () and moves in a medium that gives a damping coefficient of ½. If the mass
is set in motion with an initial velocity of 3 and is stretched initially to a length of 5. (I
purposefully removed the units- don't worry about them. Assume no conversions are
needed.)
a) Find the equation for the displacement of the spring mass at time t.
b) Write the equation for the displacement of the spring mass in phase-mode form.
c) Characterize the damping of the spring mass system as overdamped, underdamped or
critically damped. Explain how you know.
D.E. for Spring Mass Systems
k
m* g = kLo
y" +—y' + — —±y = —±F(t), y(0) = yo, y'(0) = vo
m
2
A₁ = √c₁² + C₂²
Q = tan-1
4. Given the following information determine the appropriate trial solution to find yp. Do not
solve the differential equation. Do not find the constants.
a) (D-4)2(D+ 2)y = 4e-2x
b) (D+ 1)(D² + 10D +34)y = 2e-5x cos 3x
Chapter 11 Solutions
MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS
Ch. 11.0A - In Exercises 1-10, a find the dimensions of the...Ch. 11.0A - Prob. 2ECh. 11.0A - Prob. 3ECh. 11.0A - Prob. 4ECh. 11.0A - Prob. 5ECh. 11.0A - Prob. 6ECh. 11.0A - Prob. 7ECh. 11.0A - Prob. 8ECh. 11.0A - Prob. 9ECh. 11.0A - In Exercises 1-10, a find the dimensions of the...
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