Chapter 7 The Laplace Transform 2 3 FIGURE 711 Piecewise continuous function 4 FIGURE 712 f is of exponential order 5 FIGURE 713 Three functions of exponential order 6 FIGURE 714 ID: 771621
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Chapter 7 The Laplace Transform
2
3FIGURE 7.1.1 Piecewise continuous function
4FIGURE 7.1.2 f is of exponential order
5FIGURE 7.1.3 Three functions of exponential order
6 FIGURE 7.1.4 e t is not of exponential order
7FIGURE 7.1.5 Piecewise continuous function in Example 6
8FIGURE 7.1.6 Graph for Problem 7
9FIGURE 7.1.7 Graph for Problem 8
10FIGURE 7.1.8 Graph for Problem 9
11FIGURE 7.1.9 Graph for Problem 10
12FIGURE 7.2.1 Steps in solving an IVP by the Laplace transform
13FIGURE 7.3.1 Shift on s -axis
14FIGURE 7.3.2 Graph of unit step function
15 FIGURE 7.3.3 Function is f ( t ) = ( 2 t 3 ) µ ( t 1)
16 FIGURE 7.3.4 Function is f ( t ) = 2 3 µ ( t 2) + µ ( t 3)
17FIGURE 7.3.5 Function f in Example 5
18FIGURE 7.3.6 Shift on t -axis
19FIGURE 7.3.7 Graph of function (18) in Example 9
20FIGURE 7.3.8 Embedded beam with variable load in Example 10
21FIGURE 7.3.9 Boxcar function
22FIGURE 7.3.10 Series circuit in Problem 35
23FIGURE 7.3.11 Graph for Problems 49–54
24FIGURE 7.3.12 Graph for Problem 49
25FIGURE 7.3.13 Graph for Problem 50
26FIGURE 7.3.14 Graph for Problem 51
27FIGURE 7.3.15 Graph for Problem 52
28FIGURE 7.3.16 Graph for Problem 53
29FIGURE 7.3.17 Graph for Problem 54
30FIGURE 7.3.18 Graph for Problem 61
31FIGURE 7.3.19 Graph for Problem 62
32FIGURE 7.3.20 E ( t ) in Problem 73
33FIGURE 7.3.21 E ( t ) in Problem 74
34FIGURE 7.3.22 E ( t ) in Problem 75
35FIGURE 7.3.23 E ( t ) in Problem 76
36FIGURE 7.4.1 Changing order of integration from t first to first
37FIGURE 7.4.2 LRC -series circuit
38FIGURE 7.4.3 Graph of current i ( t ) in Example 7
39FIGURE 7.4.4 Square wave in Example 8
40FIGURE 7.4.5 Graph of current i ( t ) in Example 9
41FIGURE 7.4.6 Graph for Problem 53
42FIGURE 7.4.7 Graph for Problem 54
43FIGURE 7.4.8 Graph for Problem 55
44FIGURE 7.4.9 Graph for Problem 56
45FIGURE 7.4.10 Graph for Problem 57
46FIGURE 7.4.11 Graph for Problem 58
47FIGURE 7.5.1 A golf club applies a force of large magnitude on the ball for a very short period of time
48FIGURE 7.5.2 Unit impulse
49FIGURE 7.5.3 Mass is struck at t = 2 in part (a) of Example 1
50FIGURE 7.5.4 No motion until mass is struck at t = 2 in part (b) of Example 1
51FIGURE 7.5.5 Beam embedded at its left end and free at its right end
52FIGURE 7.5.6 Beam embedded at both ends
53FIGURE 7.6.1 Coupled spring/mass system
54FIGURE 7.6.2 Displacements of the two masses in Example 1
55FIGURE 7.6.3 Electrical network
56FIGURE 7.6.4 Double pendulum
57FIGURE 7.6.5 Positions of masses on double pendulum at various times in Example 3
58FIGURE 7.6.6 Coupled springs in Problem 14
59FIGURE 7.6.7 Network in Problem 15
60FIGURE 7.6.8 Network in Problem 16
61FIGURE 7.6.9 Network in Problem 20
62FIGURE 7.R.1 Graph for Problems 25–28
63FIGURE 7.R.2 Graph for Problem 25
64FIGURE 7.R.3 Graph for Problem 26
65FIGURE 7.R.4 Graph for Problem 27
66FIGURE 7.R.5 Graph for Problem 28
67FIGURE 7.R.6 Graph for Problem 29
68FIGURE 7.R.7 Graph for Problem 30
69FIGURE 7.R.8 Graph for Problem 31
70FIGURE 7.R.9 Graph for Problem 32
71FIGURE 7.R.10 Graph for Problem 39
72FIGURE 7.R.11 Beam on elastic foundation in Problem 48
73FIGURE 7.R.12 Coupled pendulums in Problem 49
74FIGURE 7.R.13 Projectile in Problem 51