Modeling with Higher-Order Differential Equations Chapter 5 Modeling with Higher-Order Differential Equations

FIGURE 5.1.1 Spring/mass system

FIGURE 5.1.2 Direction below the equilibrium position is positive

FIGURE 5.1.3 A relationship between c1 > 0, c2 > 0 and phase angle 

FIGURE 5.1.4 Simple harmonic motion

FIGURE 5.1.5 Parallel springs

FIGURE 5.1.6 Springs in series

FIGURE 5.1.7 Damping devices

FIGURE 5.1.8 Motion of an overdamped system

FIGURE 5.1.9 Motion of a critically damped system

FIGURE 5.1.10 Motion of an underdamped system

FIGURE 5.1.11 Overdamped system in Example 3

FIGURE 5.1.12 Critically damped system in Example 4

FIGURE 5.1.13 Oscillatory vertical motion of the support

FIGURE 5.1.14 Graph of solution in (28) of Example 6

FIGURE 5.1.15 Graph of solution in Example 7 for various initial velocities x1

FIGURE 5.1.16 Pure resonance

FIGURE 5.1.17 LRC-series circuit

FIGURE 5.1.18 Graph for Problem 21

FIGURE 5.1.19 Graph for Problem 22

FIGURE 5.1.20 Graph for Problem 23

FIGURE 5.1.21 Graph for Problem 24

FIGURE 5.1.22 Oscillating support in Problem 39

FIGURE 5.1.23 Beats phenomenon in Problem 45

FIGURE 5.2.1 Deflection of a homogeneous beam

FIGURE 5.2.2 Beams with various end conditions

TABLE 5.2.1

FIGURE 5.2.3 Deflection curve for BVP in Example 1

FIGURE 5.2.4 Graphs of eigenfunctions yn = sin(nx/L), for n = 1, 2, 3, 4, 5

FIGURE 5.2.5 Elastic column buckling under a compressive force

FIGURE 5.2.6 Deflection curves corresponding to compressive forces P1, P2, P3

FIGURE 5.2.7 Rotating string and forces acting on it

FIGURE 5.2.8 Deflection of cantilever beam in Problem 7

FIGURE 5.2.9 Deflection of vertical column in Problem 24

FIGURE 5.2.10 Concentric spheres in Problem 29

FIGURE 5.2.11 Circular ring in Problem 30

FIGURE 5.2.12 Propeller shaft of the battleship USS Missouri

FIGURE 5.3.1 Hard and soft springs

FIGURE 5.3.2 Numerical solution curves

FIGURE 5.3.3 Simple pendulum

FIGURE 5.3.4 In Example 2, oscillating pendulum in (b); whirling pendulum in (c)

FIGURE 5.3.5 Shape of hanging telephone wires is a catenary

FIGURE 5.3.6 Distance to rocket is large compared to R.

FIGURE 5.3.7 Chain pulled upward by a constant force in Example 4

FIGURE 5.3.8 Graph of (21) in Example 4

FIGURE 5.3.9 Pursuit curve in Problem 17

FIGURE 5.3.10 Pursuit curve in Problem 18

FIGURE 5.3.11 Ballistic pendulum in Problem 19

FIGURE 5.3.12 Airplane drop in Problem 20

FIGURE 5.R.1 Rotating rod in Problem 24

FIGURE 5.R.2 Sliding spring/mass system in Problem 25

FIGURE 5.R.3 Double spring system in Problem 26

FIGURE 5.R.4 Spring pendulum in Problem 30

FIGURE 5.R.5 Pendulum in Problem 31

FIGURE 5.R.6 Collapse of the Tacoma Narrows Suspension Bridge