BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Show that if ω0ω, but ω/ω0 is a rational number, then the motion described by Equation 6 is periodic.

To determine

To show: If ω0ω , but ωω0 is a rational number, then the motion described by x(t)=c1cosωt+c2sinωt+F0m(ω2ω02)cosω0t is periodic.

Explanation

Given data:

x(t)=c1cosωt+c2sinωt+F0m(ω2ω02)cosω0t , ω0ω , ωω0

Consider expression as follows.

x(t)=c1cosωt+c2sinωt+F0m(ω2ω02)cosω0t (1)

Consider the value of f(t) and g(t) as follows.

f(t)=c1cosωt+c2sinωtg(t)=F0m(ω2ω02)cosω0t

Substitute f(t) for c1cosωt+c2sinωt and g(t) for F0m(ω2ω02)cosω0t in equation (1),

x(t)=f(t)+g(t) (2)

The function f(t) is periodic with period 2πω .

If ω0ω , then the function g(t) is periodic with period 2πω0 .

Consider the rational number as ab where a and b are non-zero integers.

If ωω0 is rational number then ωω0=ab .

ωω0=aba=bωω0

Consider t is periodic with period a2πω .

Modify equation (2) as follows.

x(t+a2πω)=f(t+a2πω)+g(t+a2πω) (3)

Since, function f(t) is periodic with period 2πω , f(t+a2πω) is same as f(t) .

Substitute f(t) for f(t+a2πω) in equation (3),

x(t+a2πω)=f(t)+g(t+a2πω) (4)

Find the value of g(t+a2πω)

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 17 Solutions

Show all chapter solutions add
Sect-17.1 P-11ESect-17.1 P-12ESect-17.1 P-13ESect-17.1 P-14ESect-17.1 P-15ESect-17.1 P-16ESect-17.1 P-17ESect-17.1 P-18ESect-17.1 P-19ESect-17.1 P-20ESect-17.1 P-21ESect-17.1 P-22ESect-17.1 P-23ESect-17.1 P-24ESect-17.1 P-25ESect-17.1 P-26ESect-17.1 P-27ESect-17.1 P-28ESect-17.1 P-29ESect-17.1 P-30ESect-17.1 P-31ESect-17.1 P-32ESect-17.1 P-33ESect-17.1 P-34ESect-17.2 P-1ESect-17.2 P-2ESect-17.2 P-3ESect-17.2 P-4ESect-17.2 P-5ESect-17.2 P-6ESect-17.2 P-7ESect-17.2 P-8ESect-17.2 P-9ESect-17.2 P-10ESect-17.2 P-11ESect-17.2 P-12ESect-17.2 P-13ESect-17.2 P-14ESect-17.2 P-15ESect-17.2 P-16ESect-17.2 P-17ESect-17.2 P-18ESect-17.2 P-19ESect-17.2 P-20ESect-17.2 P-21ESect-17.2 P-22ESect-17.2 P-23ESect-17.2 P-24ESect-17.2 P-25ESect-17.2 P-26ESect-17.2 P-27ESect-17.2 P-28ESect-17.3 P-1ESect-17.3 P-2ESect-17.3 P-3ESect-17.3 P-4ESect-17.3 P-5ESect-17.3 P-6ESect-17.3 P-7ESect-17.3 P-8ESect-17.3 P-9ESect-17.3 P-10ESect-17.3 P-11ESect-17.3 P-12ESect-17.3 P-13ESect-17.3 P-14ESect-17.3 P-15ESect-17.3 P-16ESect-17.3 P-17ESect-17.3 P-18ESect-17.4 P-1ESect-17.4 P-2ESect-17.4 P-3ESect-17.4 P-4ESect-17.4 P-5ESect-17.4 P-6ESect-17.4 P-7ESect-17.4 P-8ESect-17.4 P-9ESect-17.4 P-10ESect-17.4 P-11ESect-17.4 P-12ECh-17 P-1RCCCh-17 P-2RCCCh-17 P-3RCCCh-17 P-4RCCCh-17 P-5RCCCh-17 P-1RQCh-17 P-2RQCh-17 P-3RQCh-17 P-4RQCh-17 P-1RECh-17 P-2RECh-17 P-3RECh-17 P-4RECh-17 P-5RECh-17 P-6RECh-17 P-7RECh-17 P-8RECh-17 P-9RECh-17 P-10RECh-17 P-11RECh-17 P-12RECh-17 P-13RECh-17 P-14RECh-17 P-15RECh-17 P-16RECh-17 P-17RECh-17 P-18RECh-17 P-19RECh-17 P-20RECh-17 P-21RE

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

In Exercises 35-42, find functions f and g such that h = g f. (Note: The answer is not unique.) 42. h(x)=12x+1...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Suppose in an estimation of a root of f(x) = 0 we make an initial guess x1 and it turns out that f'′(x1) = 0. W...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th