Explanation 1) Concept: Use Hooke’s law to obtain the value of constant k , then find the position of the mass after t seconds by solving the second order differential equation m d 2 x d t 2 + k x = 0 … … . . i 2) Hooke’s law: The force required to maintain a spring stretched x units beyond its natural length is proportional to x : f x = k x where k is a positive constant called the spring constant 3) Given: F = 25 N , m = 5 , x 0 = 0.35 , x ' 0 = 0 4) Calculations: From Hooke’s law, the force required to stretch the spring is k 0.25 = 25 So k = 25 0 . 25 = 100 Using this value of spring constant k , together with m = 5 in equation ( i ) , The differential equation is 5 d 2 x d t 2 + 100 x = 0 The auxiliary equation is 5 r 2 + 100 = 0 Solving for r , r 2 = - 20 Therefore, the roots are r = ± 2 5 i So, the general solution to the differential equation is x t = c 1 cos ⁡ 2 5 t + c 2 sin ⁡ 2 5 t … … … i i It is given that x 0 = 1

8th Edition

ISBN: 9781285740621

Author: James Stewart

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Videos

Question

Chapter 17.3, Problem 1E

To determine

To find:

The position of the mass after t seconds

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 17.2, Problem 28E

Chapter 17.3, Problem 2E

Chapter 17 Solutions

Calculus (MindTap Course List)

Ch. 17.1 - Solve the differential equation. yy6y=0 Ch. 17.1 - Solve the differential equation. y6y+9y=0 Ch. 17.1 - Solve the differential equation. y+2y=0 Ch. 17.1 - Solve the differential equation. y+y12y=0 Ch. 17.1 - Solve the differential equation. 4y+4y+y=0 Ch. 17.1 - Solve the differential equation. 9y+4y=0 Ch. 17.1 - Solve the differential equation. 3y=4y Ch. 17.1 - Solve the differential equation. y=y Ch. 17.1 - Solve the differential equation. y4y+13y=0 Ch. 17.1 - Prob. 10E

Ch. 17.1 - Prob. 11E Ch. 17.1 - Prob. 12E Ch. 17.1 - Prob. 13E Ch. 17.1 - Prob. 14E Ch. 17.1 - Prob. 15E Ch. 17.1 - Prob. 16E Ch. 17.1 - Prob. 17E Ch. 17.1 - Prob. 18E Ch. 17.1 - Prob. 19E Ch. 17.1 - Prob. 20E Ch. 17.1 - Prob. 21E Ch. 17.1 - Prob. 22E Ch. 17.1 - Prob. 23E Ch. 17.1 - Prob. 24E Ch. 17.1 - Prob. 25E Ch. 17.1 - Prob. 26E Ch. 17.1 - Prob. 27E Ch. 17.1 - Prob. 28E Ch. 17.1 - Prob. 29E Ch. 17.1 - Prob. 30E Ch. 17.1 - Prob. 31E Ch. 17.1 - Prob. 32E Ch. 17.1 - Let L be a nonzero real number. a Show that the...Ch. 17.1 - Prob. 34E Ch. 17.1 - Consider the boundary-value problem...Ch. 17.2 - Solve the differential equation or initial-value...Ch. 17.2 - Prob. 2E Ch. 17.2 - Prob. 3E Ch. 17.2 - Prob. 4E Ch. 17.2 - Prob. 5E Ch. 17.2 - Prob. 6E Ch. 17.2 - Prob. 7E Ch. 17.2 - Prob. 8E Ch. 17.2 - Prob. 9E Ch. 17.2 - Prob. 10E Ch. 17.2 - Prob. 11E Ch. 17.2 - Prob. 12E Ch. 17.2 - Write a trial solution for the method of...Ch. 17.2 - Prob. 14E Ch. 17.2 - Prob. 15E Ch. 17.2 - Prob. 16E Ch. 17.2 - Prob. 17E Ch. 17.2 - Write a trial solution for the method of...Ch. 17.2 - Prob. 19E Ch. 17.2 - Prob. 20E Ch. 17.2 - Prob. 21E Ch. 17.2 - Prob. 22E Ch. 17.2 - Prob. 23E Ch. 17.2 - Prob. 24E Ch. 17.2 - Prob. 25E Ch. 17.2 - Prob. 26E Ch. 17.2 - Prob. 27E Ch. 17.2 - Prob. 28E Ch. 17.3 - Prob. 1E Ch. 17.3 - Prob. 2E Ch. 17.3 - Prob. 3E Ch. 17.3 - Prob. 4E Ch. 17.3 - Prob. 5E Ch. 17.3 - For the spring in Exercise 4, find the damping...Ch. 17.3 - Prob. 7E Ch. 17.3 - Prob. 8E Ch. 17.3 - Prob. 9E Ch. 17.3 - Prob. 10E Ch. 17.3 - Prob. 11E Ch. 17.3 - Prob. 12E Ch. 17.3 - A series circuit consists of a resistor with R=20,...Ch. 17.3 - Prob. 14E Ch. 17.3 - Prob. 15E Ch. 17.3 - Prob. 16E Ch. 17.3 - Prob. 17E Ch. 17.3 - The figure shows a pendulum with length L and the...Ch. 17.4 - Prob. 1E Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Prob. 3E Ch. 17.4 - Prob. 4E Ch. 17.4 - Prob. 5E Ch. 17.4 - Prob. 6E Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Prob. 9E Ch. 17.4 - Prob. 10E Ch. 17.4 - Prob. 11E Ch. 17.4 - The solution of the initial-value problem...Ch. 17.R - Prob. 1CC Ch. 17.R - Prob. 2CC Ch. 17.R - Prob. 3CC Ch. 17.R - Prob. 4CC Ch. 17.R - Prob. 5CC Ch. 17.R - Prob. 1TFQ Ch. 17.R - Prob. 2TFQ Ch. 17.R - Prob. 3TFQ Ch. 17.R - Prob. 4TFQ Ch. 17.R - Prob. 1E Ch. 17.R - Prob. 2E Ch. 17.R - Prob. 3E Ch. 17.R - Prob. 4E Ch. 17.R - Prob. 5E Ch. 17.R - Prob. 6E Ch. 17.R - Prob. 7E Ch. 17.R - Prob. 8E Ch. 17.R - Prob. 9E Ch. 17.R - Solve the differential equation....Ch. 17.R - Prob. 11E Ch. 17.R - Solve the initial-value problem....Ch. 17.R - Prob. 13E Ch. 17.R - Solve the initial-value problem....Ch. 17.R - Prob. 15E Ch. 17.R - Prob. 16E Ch. 17.R - Prob. 17E Ch. 17.R - Use power series to solve the initial-value...Ch. 17.R - Prob. 19E Ch. 17.R - Prob. 20E Ch. 17.R - Assume that the earth is a solid sphere of uniform...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:9781285463247

Author:David Poole

Publisher:Cengage Learning

Trigonometry (MindTap Course List)

Trigonometry

ISBN:9781337278461

Author:Ron Larson

Publisher:Cengage Learning

SEE MORE TEXTBOOKS

Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY

The position of the mass after t seconds

Solution Summary: The author explains Hooke's law, where the force required to maintain a spring stretched beyond its natural length is proportional to x.

Concept explainers

Videos

To find: The position of the mass after t seconds

Want to see the full answer?

Chapter 17 Solutions

To find:

The position of the mass after t seconds