- 17.3.1: A spring has natural length and a mass. A force of is needed to kee...
- 17.3.2: A spring with an mass is kept stretched beyond its natural length b...
- 17.3.3: A spring with a mass of 2 kg has damping constant 14, and a force o...
- 17.3.4: A force of 13 N is needed to keep a spring with a 2-kg mass stretch...
- 17.3.5: For the spring in Exercise 3, find the mass that would produce crit...
- 17.3.6: For the spring in Exercise 4, find the damping constant that would ...
- 17.3.7: A spring has a mass of 1 kg and its spring constant is . The spring...
- 17.3.8: A spring has a mass of 1 kg and its damping constant is The spring ...
- 17.3.9: . Suppose a spring has mass and spring constant and let . Suppose t...
- 17.3.10: As in Exercise 9, consider a spring with mass , spring con stant , ...
- 17.3.11: Show that if , but is a rational number, then the motion described ...
- 17.3.12: Consider a spring subject to a frictional or damping force. (a) In ...
- 17.3.13: A series circuit consists of a resistor with , an inductor with H, ...
- 17.3.14: A series circuit contains a resistor with , an inductor with H, a c...
- 17.3.15: The battery in Exercise 13 is replaced by a generator producing a v...
- 17.3.16: The battery in Exercise 14 is replaced by a generator pro ducing a ...
- 17.3.17: Verify that the solution to Equation 1 can be written in the form .
- 17.3.18: The figure shows a pendulum with length L and the angle from the ve...
Solutions for Chapter 17.3: Applications of Second-Order Differential Equations
Full solutions for Calculus: Early Transcendentals | 7th Edition
A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.
Convergence of a series
A series aqk=1 ak converges to a sum S if imn: q ank=1ak = S
A set with no elements
equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)
Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).
General form (of a line)
Ax + By + C = 0, where A and B are not both zero.
Initial side of an angle
See Power function.
The diagonal from the top left to the bottom right of a square matrix
Order of an m x n matrix
The order of an m x n matrix is m x n.
In an experimental study, an inactive treatment that is equivalent to the active treatment in every respect except for the factor about which an inference is to be made. Subjects in a blind experiment do not know if they have been given the active treatment or the placebo.
Computer-generated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random
An equation found by regression and which can be used to predict unknown values.
A transformation that leaves the basic shape of a graph unchanged.
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the right-hand end point of each subinterval.
Set of all possible outcomes of an experiment.
A number that measures a quantitative variable for a sample from a population.
Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.
A mean calculated in such a way that some elements of the data set have higher weights (that is, are counted more strongly in determining the mean) than others.
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.