Differential Equations with Boundary-Value Problems (MindTap Course List)
9th Edition
ISBN: 9781305965799
Author: Dennis G. Zill
Publisher: Cengage Learning
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Chapter 14, Problem 20RE
To determine
To solve: The boundary value problem under given boundary conditions.
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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
9.7 Given the equations
0.5x₁-x2=-9.5
1.02x₁ - 2x2 = -18.8
(a) Solve graphically.
(b) Compute the determinant.
(c) On the basis of (a) and (b), what would you expect regarding
the system's condition?
(d) Solve by the elimination of unknowns.
(e) Solve again, but with a modified slightly to 0.52. Interpret
your results.
Chapter 14 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
Ch. 14.1 - (a) Show that erf(t)=10ted. (b) Use part (a), the...Ch. 14.1 - Prob. 2ECh. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - Use the third and fifth entries in Table 14.1.1 to...
Ch. 14.1 - Prob. 11ECh. 14.1 - Prob. 12ECh. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.2 - A string is stretched along the x-axis between (0,...Ch. 14.2 - Prob. 2ECh. 14.2 - The displacement of a semi-infinite elastic string...Ch. 14.2 - Prob. 4ECh. 14.2 - Prob. 5ECh. 14.2 - The displacement u(x, t) of a string that is...Ch. 14.2 - Prob. 7ECh. 14.2 - Prob. 8ECh. 14.2 - Prob. 9ECh. 14.2 - Prob. 10ECh. 14.2 - Prob. 11ECh. 14.2 - Prob. 12ECh. 14.2 - Prob. 13ECh. 14.2 - In Problems 1118 use the Laplace transform to...Ch. 14.2 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - Prob. 17ECh. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.2 - Show that a solution of the boundary-value problem...Ch. 14.2 - Prob. 21ECh. 14.2 - If there is a heat transfer from the lateral...Ch. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - Prob. 27ECh. 14.2 - Prob. 28ECh. 14.2 - Prob. 29ECh. 14.2 - Prob. 30ECh. 14.3 - In Problems 16 find the Fourier integral...Ch. 14.3 - In Problems 16 find the Fourier integral...Ch. 14.3 - In Problems 16 find the Fourier integral...Ch. 14.3 - In Problems 16 find the Fourier integral...Ch. 14.3 - In Problems 16 find the Fourier integral...Ch. 14.3 - In Problems 1-6 find the Fourier integral...Ch. 14.3 - In Problems 712 represent the given function by an...Ch. 14.3 - Prob. 8ECh. 14.3 - Prob. 9ECh. 14.3 - Prob. 10ECh. 14.3 - Prob. 11ECh. 14.3 - Prob. 12ECh. 14.3 - Prob. 13ECh. 14.3 - Prob. 14ECh. 14.3 - Prob. 15ECh. 14.3 - In Problems 1316 find the cosine and sine integral...Ch. 14.3 - In Problems 17 and 18 solve the given integral...Ch. 14.3 - Prob. 18ECh. 14.3 - Prob. 19ECh. 14.3 - Prob. 20ECh. 14.4 - In Problems 1-21 and 24-26 use the Fourier...Ch. 14.4 - Prob. 2ECh. 14.4 - In Problems 121 and 2426 use the Fourier integral...Ch. 14.4 - Prob. 4ECh. 14.4 - Prob. 5ECh. 14.4 - In Problems 121 and 2426 use the Fourier integral...Ch. 14.4 - Prob. 7ECh. 14.4 - In Problems 121 and 2426 use the Fourier integral...Ch. 14.4 - Prob. 9ECh. 14.4 - Prob. 10ECh. 14.4 - Prob. 11ECh. 14.4 - Prob. 12ECh. 14.4 - Prob. 13ECh. 14.4 - Prob. 14ECh. 14.4 - Prob. 15ECh. 14.4 - Prob. 16ECh. 14.4 - Prob. 17ECh. 14.4 - In Problems 121 and 2426 use the Fourier integral...Ch. 14.4 - Prob. 19ECh. 14.4 - Prob. 20ECh. 14.4 - Prob. 21ECh. 14.4 - Prob. 22ECh. 14.4 - Prob. 23ECh. 14.4 - Prob. 24ECh. 14.4 - Prob. 25ECh. 14.4 - In Problems 121 and 2426 use the Fourier integral...Ch. 14.4 - Discussion problems 27. (a) Suppose...Ch. 14 - In Problems 1-20 solve the given boundary-value...Ch. 14 - In Problems 1-20 solve the given boundary-value...Ch. 14 - Prob. 3RECh. 14 - Prob. 4RECh. 14 - In Problems 1-20 solve the given boundary-value...Ch. 14 - Prob. 6RECh. 14 - Prob. 7RECh. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - Prob. 10RECh. 14 - Prob. 11RECh. 14 - Prob. 12RECh. 14 - Prob. 13RECh. 14 - Prob. 14RECh. 14 - Prob. 15RECh. 14 - Prob. 16RECh. 14 - Prob. 17RECh. 14 - Prob. 18RECh. 14 - Prob. 19RECh. 14 - Prob. 20RECh. 14 - Prob. 21RE
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