Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
5th Edition
ISBN: 9780321816252
Author: C. Henry Edwards, David E. Penney, David Calvis
Publisher: PEARSON
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Textbook Question
Chapter 7.3, Problem 39P
Problems 39 and 40 illustrate Iwo types of resonance in a mass-spring-dashpot system with given external force F(t) and with the initial conditions
Suppose that m = 1, k = 9, c = 0, and F(t) = 6 cos 3t. Use the inverse transform given in Eq. (16) to derive the solution x(t) = t sin 3t. Construct a figure that illustrates the resonance that occurs.
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3. (i) Using the definition of the line integral of a vector field, calculate the
line integral
L³
F.dy
of the vector field F: R² → R² given by
F(x, y) = (y, x),
and where the curve & is the unit semi-circle centred at the origin, located in
the upper half-plane and oriented in the anticlockwise direction.
Hint. Represent the curve y as the join of two curves y = 71 + 1/2 (see Example 8.9
in the Notes).
[20 Marks]
(ii) Calculate the same integral using Green's Theorem.
[10 Marks]
1. Evaluate the integral
↓ f(x, y)dxdy,
of function f R² →R over the domain DC R2, where:
f(x, y) = 2x + y
and D is the is the triangle with vertices (0, -1), (1,0) and (0,2).
Hint. Represent D in the form D = {(x, y) = R² : x = (a, b), g(x) < y < h(x)} for
some a
2. (i) Describe with a sketch the trace of the following curve in R²
(t) = (t² sin(t), t2 cos(t)),
(€ -2,2]).
[15 Marks]
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[25 Marks]
Chapter 7 Solutions
Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
Ch. 7.1 - Apply the definition in (1) to find directly tile...Ch. 7.1 - Prob. 2PCh. 7.1 - Prob. 3PCh. 7.1 - Prob. 4PCh. 7.1 - Prob. 5PCh. 7.1 - Prob. 6PCh. 7.1 - Prob. 7PCh. 7.1 - Prob. 8PCh. 7.1 - Prob. 9PCh. 7.1 - Prob. 10P
Ch. 7.1 - Prob. 11PCh. 7.1 - Prob. 12PCh. 7.1 - Prob. 13PCh. 7.1 - Prob. 14PCh. 7.1 - Prob. 15PCh. 7.1 - Prob. 16PCh. 7.1 - Prob. 17PCh. 7.1 - Prob. 18PCh. 7.1 - Prob. 19PCh. 7.1 - Prob. 20PCh. 7.1 - Prob. 21PCh. 7.1 - Prob. 22PCh. 7.1 - Prob. 23PCh. 7.1 - Prob. 24PCh. 7.1 - Prob. 25PCh. 7.1 - Prob. 26PCh. 7.1 - Prob. 27PCh. 7.1 - Prob. 28PCh. 7.1 - Prob. 29PCh. 7.1 - Prob. 30PCh. 7.1 - Prob. 31PCh. 7.1 - Prob. 32PCh. 7.1 - Prob. 33PCh. 7.1 - Prob. 34PCh. 7.1 - Prob. 35PCh. 7.1 - Prob. 36PCh. 7.1 - Given a0, let f(t)=1 if 0__1a,f(t)=0 if t__a....Ch. 7.1 - Given that 0ab. Let f(t)=1 if a__tb,f(t)=0 if...Ch. 7.1 - Prob. 39PCh. 7.1 - Prob. 40PCh. 7.1 - Prob. 41PCh. 7.1 - Given constants a and b. define h(t) for t__0 by...Ch. 7.2 - Prob. 1PCh. 7.2 - Prob. 2PCh. 7.2 - Prob. 3PCh. 7.2 - Prob. 4PCh. 7.2 - Prob. 5PCh. 7.2 - Prob. 6PCh. 7.2 - Prob. 7PCh. 7.2 - Prob. 8PCh. 7.2 - Prob. 9PCh. 7.2 - Prob. 10PCh. 7.2 - Prob. 11PCh. 7.2 - Prob. 12PCh. 7.2 - Prob. 13PCh. 7.2 - Prob. 14PCh. 7.2 - Prob. 15PCh. 7.2 - Prob. 16PCh. 7.2 - Prob. 17PCh. 7.2 - Prob. 18PCh. 7.2 - Prob. 19PCh. 7.2 - Prob. 20PCh. 7.2 - Prob. 21PCh. 7.2 - Prob. 22PCh. 7.2 - Prob. 23PCh. 7.2 - Prob. 24PCh. 7.2 - Prob. 25PCh. 7.2 - Prob. 26PCh. 7.2 - Prob. 27PCh. 7.2 - Prob. 28PCh. 7.2 - Prob. 29PCh. 7.2 - Prob. 30PCh. 7.2 - Prob. 31PCh. 7.2 - Prob. 32PCh. 7.2 - Prob. 33PCh. 7.2 - Prob. 34PCh. 7.2 - Prob. 35PCh. 7.2 - Prob. 36PCh. 7.2 - Prob. 37PCh. 7.3 - Prob. 1PCh. 7.3 - Prob. 2PCh. 7.3 - Prob. 3PCh. 7.3 - Prob. 4PCh. 7.3 - Prob. 5PCh. 7.3 - Prob. 6PCh. 7.3 - Prob. 7PCh. 7.3 - Prob. 8PCh. 7.3 - Prob. 9PCh. 7.3 - Prob. 10PCh. 7.3 - Prob. 11PCh. 7.3 - Prob. 12PCh. 7.3 - Prob. 13PCh. 7.3 - Prob. 14PCh. 7.3 - Prob. 15PCh. 7.3 - Prob. 16PCh. 7.3 - Prob. 17PCh. 7.3 - Prob. 18PCh. 7.3 - Prob. 19PCh. 7.3 - Prob. 20PCh. 7.3 - Prob. 21PCh. 7.3 - Prob. 22PCh. 7.3 - Prob. 23PCh. 7.3 - Prob. 24PCh. 7.3 - Prob. 25PCh. 7.3 - Prob. 26PCh. 7.3 - Prob. 27PCh. 7.3 - Prob. 28PCh. 7.3 - Prob. 29PCh. 7.3 - Prob. 30PCh. 7.3 - Prob. 31PCh. 7.3 - Prob. 32PCh. 7.3 - Prob. 33PCh. 7.3 - Prob. 34PCh. 7.3 - Prob. 35PCh. 7.3 - Prob. 36PCh. 7.3 - Prob. 37PCh. 7.3 - Prob. 38PCh. 7.3 - Problems 39 and 40 illustrate Iwo types of...Ch. 7.3 - Problems 39 and 40 illustrate Iwo types of...Ch. 7.4 - Find the convolution f(t)g(t) in Problems 1...Ch. 7.4 - Prob. 2PCh. 7.4 - Prob. 3PCh. 7.4 - Prob. 4PCh. 7.4 - Prob. 5PCh. 7.4 - Prob. 6PCh. 7.4 - Prob. 7PCh. 7.4 - Prob. 8PCh. 7.4 - Prob. 9PCh. 7.4 - Prob. 10PCh. 7.4 - Prob. 11PCh. 7.4 - Prob. 12PCh. 7.4 - Prob. 13PCh. 7.4 - Prob. 14PCh. 7.4 - Prob. 15PCh. 7.4 - Prob. 16PCh. 7.4 - Prob. 17PCh. 7.4 - Prob. 18PCh. 7.4 - Prob. 19PCh. 7.4 - Prob. 20PCh. 7.4 - Prob. 21PCh. 7.4 - Prob. 22PCh. 7.4 - Prob. 23PCh. 7.4 - Prob. 24PCh. 7.4 - Prob. 25PCh. 7.4 - Prob. 26PCh. 7.4 - Prob. 27PCh. 7.4 - Prob. 28PCh. 7.4 - Prob. 29PCh. 7.4 - Prob. 30PCh. 7.4 - Prob. 31PCh. 7.4 - Prob. 32PCh. 7.4 - Prob. 33PCh. 7.4 - Prob. 34PCh. 7.4 - Prob. 35PCh. 7.4 - Prob. 36PCh. 7.4 - Prob. 37PCh. 7.4 - Prob. 38PCh. 7.4 - Prob. 39PCh. 7.4 - Prob. 40PCh. 7.4 - Prob. 41PCh. 7.5 - Prob. 1PCh. 7.5 - Prob. 2PCh. 7.5 - Prob. 3PCh. 7.5 - Prob. 4PCh. 7.5 - Prob. 5PCh. 7.5 - Prob. 6PCh. 7.5 - Prob. 7PCh. 7.5 - Prob. 8PCh. 7.5 - Prob. 9PCh. 7.5 - Prob. 10PCh. 7.5 - Prob. 11PCh. 7.5 - Prob. 12PCh. 7.5 - Prob. 13PCh. 7.5 - Prob. 14PCh. 7.5 - Prob. 15PCh. 7.5 - Prob. 16PCh. 7.5 - Prob. 17PCh. 7.5 - Prob. 18PCh. 7.5 - Prob. 19PCh. 7.5 - Prob. 20PCh. 7.5 - Prob. 21PCh. 7.5 - Prob. 22PCh. 7.5 - Prob. 23PCh. 7.5 - Prob. 24PCh. 7.5 - Prob. 25PCh. 7.5 - Prob. 26PCh. 7.5 - Let g(t) be the staircase function of Fig. 7.5.15....Ch. 7.5 - Suppose that f(i) is a periodic function of period...Ch. 7.5 - Suppose that f(t) is the half-wave rectification...Ch. 7.5 - Let g(t)=u(tk)f(tk), where f(t) is the function of...Ch. 7.5 - Prob. 31PCh. 7.5 - Prob. 32PCh. 7.5 - Prob. 33PCh. 7.5 - Prob. 34PCh. 7.5 - Prob. 35PCh. 7.5 - Prob. 36PCh. 7.5 - Prob. 37PCh. 7.5 - Prob. 38PCh. 7.5 - Prob. 39PCh. 7.5 - Prob. 40PCh. 7.5 - Prob. 41PCh. 7.5 - Prob. 42PCh. 7.6 - Prob. 1PCh. 7.6 - Prob. 2PCh. 7.6 - Prob. 3PCh. 7.6 - Prob. 4PCh. 7.6 - Prob. 5PCh. 7.6 - Prob. 6PCh. 7.6 - Prob. 7PCh. 7.6 - Prob. 8PCh. 7.6 - Prob. 9PCh. 7.6 - Prob. 10PCh. 7.6 - Prob. 11PCh. 7.6 - Prob. 12PCh. 7.6 - Prob. 13PCh. 7.6 - Prob. 14PCh. 7.6 - This problem deals with a mass in on a spring...Ch. 7.6 - Prob. 16PCh. 7.6 - Prob. 17PCh. 7.6 - Prob. 18PCh. 7.6 - Prob. 19PCh. 7.6 - Repeat Problem 19, except suppose that the switch...Ch. 7.6 - Prob. 21PCh. 7.6 - Prob. 22P
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