- 5.3.1: In 14 the given differential equation is model of an undamped sprin...
- 5.3.2: In 14 the given differential equation is model of an undamped sprin...
- 5.3.3: In 14 the given differential equation is model of an undamped sprin...
- 5.3.4: In 14 the given differential equation is model of an undamped sprin...
- 5.3.5: In 3, suppose the mass is released from the initial position x(0) 1...
- 5.3.6: In 3, suppose the mass is released from an initial position x(0) x0...
- 5.3.7: Find a linearization of the differential equation in 4.
- 5.3.8: Consider the model of an undamped nonlinear spring/mass system give...
- 5.3.9: In 9 and 10 the given differential equation is a model of a damped ...
- 5.3.10: In 9 and 10 the given differential equation is a model of a damped ...
- 5.3.11: The model mx kx k1x3 F0cos vt of an undamped periodically driven sp...
- 5.3.12: (a) Find values of k1 0 for which the system in is oscillatory. (b)...
- 5.3.13: Consider the model of the free damped nonlinear pendulum given by ....
- 5.3.14: (a) Use the substitution v dydt to solve (13) for v in terms of y. ...
- 5.3.15: (a) In Example 4, how much of the chain would you intuitively expec...
- 5.3.16: A uniform chain of length L, measured in feet, is held vertically s...
- 5.3.17: In a naval exercise a ship S1 is pursued by a submarine S2 as shown...
- 5.3.18: In another naval exercise a destroyer S1 pursues a submerged submar...
- 5.3.19: Historically, in order to maintain quality control over munitions (...
- 5.3.20: As shown in Figure 5.3.11, a plane flying horizontally at a constan...
- 5.3.21: Discuss why the damping term in equation (3) is written as
- 5.3.22: (a) Experiment with a calculator to find an interval 0 u u1, where ...
- 5.3.23: Does a pendulum of length l oscillate faster on the Earth or on the...
- 5.3.24: Repeat the two parts of this time using the linear model (7)
- 5.3.25: Consider the initial-value problem for a nonlinear pendulum. Since ...
- 5.3.26: Consider a pendulum that is released from rest from an initial disp...
Solutions for Chapter 5.3: NONLINEAR MODEL
Full solutions for A First Course in Differential Equations with Modeling Applications | 10th Edition
A triangle in which all angles measure less than 90°
Speed of rotation, typically measured in radians or revolutions per unit time
A ratio equal to 1, used for unit conversion
Differentiable at x = a
Arrows that have the same magnitude and direction.
a + 0 = a, a ? 1 = a
Law of sines
sin A a = sin B b = sin C c
A graph of a polar equation r = a b sin u or r = a b cos u with a > 0 b > 0
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I
Mean (of a set of data)
The sum of all the data divided by the total number of items
Natural logarithmic function
The inverse of the exponential function y = ex, denoted by y = ln x.
The principle of experimental design that makes it possible to use the laws of probability when making inferences.
A logarithmic scale used in measuring the intensity of an earthquake.
Slope-intercept form (of a line)
y = mx + b
Solution set of an inequality
The set of all solutions of an inequality
If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.
The function that associates points on the unit circle with points on the real number line
The x-value of the left side of the viewing window,.
The scale of the tick marks on the y-axis in a viewing window.
The vector <0,0> or <0,0,0>.