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Chapter 7 The Laplace Transform
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FIGURE 7.1.1 Piecewise continuous function
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FIGURE 7.1.2 f is of exponential order
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FIGURE 7.1.3 Three functions of exponential order
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FIGURE 7.1.4 et2 is not of exponential order
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FIGURE 7.1.5 Piecewise continuous function in Example 6
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FIGURE 7.1.6 Graph for Problem 7
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FIGURE 7.1.7 Graph for Problem 8
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FIGURE 7.1.8 Graph for Problem 9
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FIGURE 7.1.9 Graph for Problem 10
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FIGURE 7.2.1 Steps in solving an IVP by the Laplace transform
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FIGURE Shift on s-axis
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FIGURE 7.3.2 Graph of unit step function
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FIGURE 7.3.3 Function is f(t) = (2t − 3 ) µ(t − 1)
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FIGURE 7.3.4 Function is f (t) = 2 − 3µ(t − 2) + µ(t − 3)
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FIGURE 7.3.5 Function f in Example 5
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FIGURE Shift on t-axis
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FIGURE 7.3.7 Graph of function (18) in Example 9
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FIGURE 7.3.8 Embedded beam with variable load in Example 10
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FIGURE 7.3.9 Boxcar function
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FIGURE 7.3.10 Series circuit in Problem 35
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FIGURE 7.3.11 Graph for Problems 49–54
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FIGURE 7.3.12 Graph for Problem 49
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FIGURE 7.3.13 Graph for Problem 50
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FIGURE 7.3.14 Graph for Problem 51
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FIGURE 7.3.15 Graph for Problem 52
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FIGURE 7.3.16 Graph for Problem 53
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FIGURE 7.3.17 Graph for Problem 54
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FIGURE 7.3.18 Graph for Problem 61
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FIGURE 7.3.19 Graph for Problem 62
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FIGURE E(t) in Problem 73
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FIGURE E(t) in Problem 74
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FIGURE E(t) in Problem 75
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FIGURE E(t) in Problem 76
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FIGURE 7.4.1 Changing order of integration from t first to first
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FIGURE 7.4.2 LRC-series circuit
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FIGURE 7.4.3 Graph of current i(t) in Example 7
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FIGURE 7.4.4 Square wave in Example 8
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FIGURE 7.4.5 Graph of current i(t) in Example 9
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FIGURE 7.4.6 Graph for Problem 53
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FIGURE 7.4.7 Graph for Problem 54
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FIGURE 7.4.8 Graph for Problem 55
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FIGURE 7.4.9 Graph for Problem 56
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FIGURE 7.4.10 Graph for Problem 57
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FIGURE 7.4.11 Graph for Problem 58
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FIGURE A golf club applies a force of large magnitude on the ball for a very short period of time
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FIGURE Unit impulse
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FIGURE 7.5.3 Mass is struck at t = 2 in part (a) of Example 1
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FIGURE 7.5.4 No motion until mass is struck at t = 2 in part (b) of Example 1
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FIGURE 7.5.5 Beam embedded at its left end and free at its right end
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FIGURE 7.5.6 Beam embedded at both ends
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FIGURE 7.6.1 Coupled spring/mass system
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FIGURE 7.6.2 Displacements of the two masses in Example 1
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FIGURE 7.6.3 Electrical network
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FIGURE 7.6.4 Double pendulum
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FIGURE 7.6.5 Positions of masses on double pendulum at various times in Example 3
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FIGURE 7.6.6 Coupled springs in Problem 14
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FIGURE 7.6.7 Network in Problem 15
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FIGURE 7.6.8 Network in Problem 16
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FIGURE 7.6.9 Network in Problem 20
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FIGURE 7.R.1 Graph for Problems 25–28
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FIGURE 7.R.2 Graph for Problem 25
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FIGURE 7.R.3 Graph for Problem 26
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FIGURE 7.R.4 Graph for Problem 27
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FIGURE 7.R.5 Graph for Problem 28
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FIGURE 7.R.6 Graph for Problem 29
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FIGURE 7.R.7 Graph for Problem 30
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FIGURE 7.R.8 Graph for Problem 31
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FIGURE 7.R.9 Graph for Problem 32
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FIGURE 7.R.10 Graph for Problem 39
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FIGURE 7.R.11 Beam on elastic foundation in Problem 48
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FIGURE 7.R.12 Coupled pendulums in Problem 49
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FIGURE 7.R.13 Projectile in Problem 51
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