Thomas' Calculus Format: Unbound (saleable) With Access Card
14th Edition
ISBN: 9780134768762
Author: Hass, Joel R.^heil, Christopher D.^weir, Maurice D.
Publisher: Prentice Hall
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Question
Chapter 17.4, Problem 15E
To determine
To find: The general solution to the Euler equation
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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 17 Solutions
Thomas' Calculus Format: Unbound (saleable) With Access Card
Ch. 17.1 - In Exercises 1−30, find the general solution of...Ch. 17.1 - In Exercises 1 – 30, find the general solution of...Ch. 17.1 - Prob. 3ECh. 17.1 - Prob. 4ECh. 17.1 - Prob. 5ECh. 17.1 - Prob. 6ECh. 17.1 - Prob. 7ECh. 17.1 - Prob. 8ECh. 17.1 - Prob. 9ECh. 17.1 - Prob. 10E
Ch. 17.1 - Prob. 11ECh. 17.1 - Prob. 12ECh. 17.1 - Prob. 13ECh. 17.1 - Prob. 14ECh. 17.1 - Prob. 15ECh. 17.1 - Prob. 16ECh. 17.1 - Prob. 17ECh. 17.1 - Prob. 18ECh. 17.1 - Prob. 19ECh. 17.1 - Prob. 20ECh. 17.1 - Prob. 21ECh. 17.1 - Prob. 22ECh. 17.1 - Prob. 23ECh. 17.1 - Prob. 24ECh. 17.1 - Prob. 25ECh. 17.1 - Prob. 26ECh. 17.1 - Prob. 27ECh. 17.1 - Prob. 28ECh. 17.1 - Prob. 29ECh. 17.1 - Prob. 30ECh. 17.1 - Prob. 31ECh. 17.1 - Prob. 32ECh. 17.1 - Prob. 33ECh. 17.1 - Prob. 34ECh. 17.1 - Prob. 35ECh. 17.1 - Prob. 36ECh. 17.1 - Prob. 37ECh. 17.1 - Prob. 38ECh. 17.1 - Prob. 39ECh. 17.1 - Prob. 40ECh. 17.1 - Prob. 41ECh. 17.1 - Prob. 42ECh. 17.1 - Prob. 43ECh. 17.1 - Prob. 44ECh. 17.1 - Prob. 45ECh. 17.1 - Prob. 46ECh. 17.1 - Prob. 47ECh. 17.1 - Prob. 48ECh. 17.1 - Prob. 49ECh. 17.1 - Prob. 50ECh. 17.1 - Prob. 51ECh. 17.1 - Prob. 52ECh. 17.1 - Prob. 53ECh. 17.1 - Prob. 54ECh. 17.1 - Prob. 55ECh. 17.1 - In Exercises 56−60, solve the initial value...Ch. 17.1 - Prob. 57ECh. 17.1 - Prob. 58ECh. 17.1 - Prob. 59ECh. 17.1 - Prob. 60ECh. 17.1 - Prob. 61ECh. 17.1 - Prob. 62ECh. 17.1 - Prob. 63ECh. 17.1 - Prob. 64ECh. 17.1 - Prob. 65ECh. 17.1 - Show that if a, b, and c are positive constants,...Ch. 17.2 - Prob. 1ECh. 17.2 - Prob. 2ECh. 17.2 - Prob. 3ECh. 17.2 - Prob. 4ECh. 17.2 - Prob. 5ECh. 17.2 - Prob. 6ECh. 17.2 - Prob. 7ECh. 17.2 - Prob. 8ECh. 17.2 - Prob. 9ECh. 17.2 - Prob. 10ECh. 17.2 - Prob. 11ECh. 17.2 - Solve the equations in Exercises 1−16 by the...Ch. 17.2 - Prob. 13ECh. 17.2 - Prob. 14ECh. 17.2 - Prob. 15ECh. 17.2 - Prob. 16ECh. 17.2 - Prob. 17ECh. 17.2 - Prob. 18ECh. 17.2 - Prob. 19ECh. 17.2 - Prob. 20ECh. 17.2 - Prob. 21ECh. 17.2 - Prob. 22ECh. 17.2 - Prob. 23ECh. 17.2 - Prob. 24ECh. 17.2 - Prob. 25ECh. 17.2 - Prob. 26ECh. 17.2 - Prob. 27ECh. 17.2 - Prob. 28ECh. 17.2 - Prob. 29ECh. 17.2 - Prob. 30ECh. 17.2 - Prob. 31ECh. 17.2 - Prob. 32ECh. 17.2 - Prob. 33ECh. 17.2 - Prob. 34ECh. 17.2 - Prob. 35ECh. 17.2 - Prob. 36ECh. 17.2 - Prob. 37ECh. 17.2 - Prob. 38ECh. 17.2 - Prob. 39ECh. 17.2 - Prob. 40ECh. 17.2 - Prob. 41ECh. 17.2 - Prob. 42ECh. 17.2 - Prob. 43ECh. 17.2 - Prob. 44ECh. 17.2 - Prob. 45ECh. 17.2 - Prob. 46ECh. 17.2 - Prob. 47ECh. 17.2 - Prob. 48ECh. 17.2 - Prob. 49ECh. 17.2 - Prob. 50ECh. 17.2 - Prob. 51ECh. 17.2 - Prob. 52ECh. 17.2 - In Exercises 53–58, verify that the given function...Ch. 17.2 - In Exercises 53–58, verify that the given function...Ch. 17.2 - Prob. 55ECh. 17.2 - Prob. 56ECh. 17.2 - Prob. 57ECh. 17.2 - Prob. 58ECh. 17.2 - Prob. 59ECh. 17.2 - Prob. 60ECh. 17.3 - Prob. 1ECh. 17.3 - Prob. 2ECh. 17.3 - A 20-lb weight is hung on an 18-in. spring and...Ch. 17.3 - Prob. 4ECh. 17.3 - Prob. 5ECh. 17.3 - Prob. 6ECh. 17.3 - Prob. 7ECh. 17.3 - Prob. 8ECh. 17.3 - Prob. 9ECh. 17.3 - Prob. 10ECh. 17.3 - Prob. 11ECh. 17.3 - Prob. 12ECh. 17.3 - Prob. 13ECh. 17.3 - Prob. 14ECh. 17.3 - Prob. 15ECh. 17.3 - Prob. 16ECh. 17.3 - Prob. 17ECh. 17.3 - Prob. 18ECh. 17.3 - Prob. 19ECh. 17.3 - Prob. 20ECh. 17.3 - Prob. 21ECh. 17.3 - Prob. 22ECh. 17.3 - Prob. 23ECh. 17.3 - Prob. 24ECh. 17.3 - Suppose L = 10 henrys, R = 10 ohms, C = 1/500...Ch. 17.3 - Prob. 26ECh. 17.4 - Prob. 1ECh. 17.4 - Prob. 2ECh. 17.4 - Prob. 3ECh. 17.4 - Prob. 4ECh. 17.4 - Prob. 5ECh. 17.4 - Prob. 6ECh. 17.4 - Prob. 7ECh. 17.4 - Prob. 8ECh. 17.4 - Prob. 9ECh. 17.4 - Prob. 10ECh. 17.4 - Prob. 11ECh. 17.4 - Prob. 12ECh. 17.4 - Prob. 13ECh. 17.4 - Prob. 14ECh. 17.4 - Prob. 15ECh. 17.4 - Prob. 16ECh. 17.4 - Prob. 17ECh. 17.4 - Prob. 18ECh. 17.4 - Prob. 19ECh. 17.4 - Prob. 20ECh. 17.4 - Prob. 21ECh. 17.4 - Prob. 22ECh. 17.4 - Prob. 23ECh. 17.4 - Prob. 24ECh. 17.4 - Prob. 25ECh. 17.4 - Prob. 26ECh. 17.4 - Prob. 27ECh. 17.4 - Prob. 28ECh. 17.4 - Prob. 29ECh. 17.4 - Prob. 30ECh. 17.5 - Prob. 1ECh. 17.5 - Prob. 2ECh. 17.5 - Prob. 3ECh. 17.5 - Prob. 4ECh. 17.5 - Prob. 5ECh. 17.5 - Prob. 6ECh. 17.5 - Prob. 7ECh. 17.5 - Prob. 8ECh. 17.5 - Prob. 9ECh. 17.5 - Prob. 10ECh. 17.5 - Prob. 11ECh. 17.5 - Prob. 12ECh. 17.5 - Prob. 13ECh. 17.5 - Prob. 14ECh. 17.5 - Prob. 15ECh. 17.5 - Prob. 16ECh. 17.5 - Prob. 17ECh. 17.5 - Prob. 18E
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