Study Guide for Stewart's Multivariable Calculus, 8th
8th Edition
ISBN: 9781305271845
Author: Stewart, James
Publisher: Brooks Cole
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Chapter 14.8, Problem 2PT
To determine
The appropriate option for the set of equations which results when finding a solution for the given information by Lagrange multipliers, from the given options
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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
3. Determine the appropriate annihilator for the given F(x).
a) F(x) = 5 cos 2x
b) F(x)=9x2e3x
Chapter 14 Solutions
Study Guide for Stewart's Multivariable Calculus, 8th
Ch. 14.1 - Which of these points is not in the domain of...Ch. 14.1 - Prob. 2PTCh. 14.1 - Each level curve (for k 0) of f(x, y) = xy is...Ch. 14.1 - Prob. 4PTCh. 14.1 - The range of f(x,y)=x+1y is: a) (,) b) [0, ) c)...Ch. 14.2 - Prob. 1PTCh. 14.2 - Prob. 2PTCh. 14.2 - Prob. 3PTCh. 14.2 - Prob. 4PTCh. 14.2 - Prob. 5PT
Ch. 14.3 - fx(a, b) is the slope of the tangent line to the...Ch. 14.3 - Prob. 2PTCh. 14.3 - Prob. 3PTCh. 14.3 - Prob. 4PTCh. 14.3 - Prob. 5PTCh. 14.3 - Prob. 6PTCh. 14.4 - Prob. 1PTCh. 14.4 - Prob. 2PTCh. 14.4 - Prob. 3PTCh. 14.4 - Prob. 4PTCh. 14.5 - Prob. 1PTCh. 14.5 - Prob. 2PTCh. 14.5 - Prob. 3PTCh. 14.5 - Find zx for z=f(x,y) defined implicity by...Ch. 14.6 - Prob. 1PTCh. 14.6 - Prob. 2PTCh. 14.6 - For z = f(x, y) and u = j, Du f(a, b) = a) fx(a,...Ch. 14.6 - Prob. 4PTCh. 14.6 - Prob. 5PTCh. 14.6 - Prob. 6PTCh. 14.7 - Prob. 1PTCh. 14.7 - Prob. 2PTCh. 14.7 - Prob. 3PTCh. 14.7 - Prob. 4PTCh. 14.8 - Prob. 1PTCh. 14.8 - Prob. 2PT
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