Differential Equations and Linear Algebra (4th Edition)
4th Edition
ISBN: 9780321964670
Author: Stephen W. Goode, Scott A. Annin
Publisher: PEARSON
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Chapter 8.7, Problem 18P
To determine
The general solution of the differential equation.
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2. The duration of the ride is 15 min.
(a) How many times does the last passenger who boarded the ride make a complete loop on the Ferris
wheel?
(b) What is the position of that passenger when the ride ends?
3. A scientist recorded the movement of a pendulum for 10 s. The scientist began recording when the pendulum
was at its resting position. The pendulum then moved right (positive displacement) and left (negative
displacement) several times. The pendulum took 4 s to swing to the right and the left and then return to its
resting position. The pendulum's furthest distance to either side was 6 in. Graph the function that represents
the pendulum's displacement as a function of time.
Answer:
f(t)
(a) Write an equation to represent the displacement of the pendulum as a function of time.
(b) Graph the function.
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A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually
cranked into the lowest position in order to exit the ride. Sine function model: h = −82.5 cos (3πt) + 97.5
where h is the height of the last passenger above the ground measured in feet and t is the time of operation of
the ride in minutes.
(a) What is the height of the last passenger at the moment of the power outage? Verify your answer by
evaluating the sine function model.
(b) Will the last passenger to board the ride need to wait in order to exit the ride? Explain.
Chapter 8 Solutions
Differential Equations and Linear Algebra (4th Edition)
Ch. 8.1 - True-False Review For Questions a-j, decide if the...Ch. 8.1 - True-False Review For Questions a-j, decide if the...Ch. 8.1 - True-False Review For Questions a-j, decide if the...Ch. 8.1 - True-False Review For Questions a-j, decide if the...Ch. 8.1 - Prob. 5TFRCh. 8.1 - Prob. 6TFRCh. 8.1 - True-False Review For Questions a-j, decide if the...Ch. 8.1 - Prob. 8TFRCh. 8.1 - Prob. 9TFRCh. 8.1 - True-False Review For Questions a-j, decide if the...
Ch. 8.1 - Problems For problem 1-4, find Ly for the given...Ch. 8.1 - Problems For problem 1-4, find Ly for the given...Ch. 8.1 - Problems For problem 1-4, find Ly for the given...Ch. 8.1 - Problems For problem 1-4, find Ly for the given...Ch. 8.1 - Problems For problem 5-9, verify that given...Ch. 8.1 - Prob. 6PCh. 8.1 - Problems For problem 5-9, verify that given...Ch. 8.1 - Problems For problem 5-9, verify that given...Ch. 8.1 - Prob. 9PCh. 8.1 - Problems For problem 10-13, compute Ker(L). L=D3x2Ch. 8.1 - For Problems 10-13, compute Ker(L). L=D2+1Ch. 8.1 - For Problem 10-13, compute ker(L). L=D2+2D15Hint:...Ch. 8.1 - For Problems 10-13, compute Ker(L). L=x2D+x.Ch. 8.1 - Problems For problems 14-15, find L1L2 and L2L1...Ch. 8.1 - Problems For problems 14-15, find L1L2 and L2L1...Ch. 8.1 - Problems If L1=D+a1(x), determine all differential...Ch. 8.1 - Problems For Problems 17-18, write the given...Ch. 8.1 - Prob. 18PCh. 8.1 - Prob. 19PCh. 8.1 - Prob. 20PCh. 8.1 - Determine which of the following sets of vectors...Ch. 8.1 - Determine which of the following sets of vectors...Ch. 8.1 - For Problems 23-26, determine two linearly...Ch. 8.1 - For Problems 23-26, determine two linearly...Ch. 8.1 - For Problems 23-26, determine two linearly...Ch. 8.1 - For Problems 23-26, determine two linearly...Ch. 8.1 - For Problems 27-31, determine three linearly...Ch. 8.1 - For Problems 27-31, determine three linearly...Ch. 8.1 - For Problems 27-31, determine three linearly...Ch. 8.1 - Prob. 30PCh. 8.1 - For Problems 27-31, determine three linearly...Ch. 8.1 - Prob. 32PCh. 8.1 - For Problems 32-33, determine four linearly...Ch. 8.1 - For Problems 34-35, determine two linearly...Ch. 8.1 - For Problems 34-35, determine two linearly...Ch. 8.1 - For Problems 34-35, determine three linearly...Ch. 8.1 - Prob. 37PCh. 8.1 - Determine a particular solution for the...Ch. 8.1 - Determine a particular solution for the...Ch. 8.1 - Prob. 40PCh. 8.1 - Determine a particular solution for the...Ch. 8.1 - Prob. 42PCh. 8.1 - Prob. 43PCh. 8.1 - Extend the proof of theorem 8.1.4 to an arbitrary...Ch. 8.1 - Prob. 45PCh. 8.1 - Let T:VW be a linear transformation, and suppose...Ch. 8.2 - True-False Review For Questions a-h, decide if the...Ch. 8.2 - True-False Review For Questions a-h, decide if the...Ch. 8.2 - Prob. 3TFRCh. 8.2 - Prob. 4TFRCh. 8.2 - True-False Review For Questions a-h, decide if the...Ch. 8.2 - Prob. 6TFRCh. 8.2 - Prob. 7TFRCh. 8.2 - Prob. 8TFRCh. 8.2 - Problems For Problems 1-3, determine a basis for...Ch. 8.2 - Prob. 2PCh. 8.2 - Problems For Problems 1-3, determine a basis for...Ch. 8.2 - Prob. 4PCh. 8.2 - Prob. 5PCh. 8.2 - Determine a basis for the solution space to y+4y=0...Ch. 8.2 - Determine a basis for the solution space to y+y=0...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 35-38, solve the given...Ch. 8.2 - Problems For Problems 35-38, solve the given...Ch. 8.2 - Problems For Problems 35-38, solve the given...Ch. 8.2 - Problems For Problems 35-38, solve the given...Ch. 8.2 - Prob. 39PCh. 8.2 - Prob. 40PCh. 8.2 - Prob. 41PCh. 8.2 - Prob. 42PCh. 8.2 - Prob. 43PCh. 8.2 - Problems Consider P(D)=y. What conditions on the...Ch. 8.2 - Prob. 45PCh. 8.2 - Prob. 46PCh. 8.2 - Prob. 47PCh. 8.2 - Prob. 48PCh. 8.2 - Prob. 49PCh. 8.2 - Prob. 50PCh. 8.2 - Prob. 51PCh. 8.2 - Prob. 54PCh. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problems, 17-32, determine the general...Ch. 8.3 - For Problems, 17-32, determine the general...Ch. 8.3 - For Problems, 17-32, determine the general...Ch. 8.3 - For Problems, 17-32, determine the general...Ch. 8.3 - For Problems, 17-32, determine the general...Ch. 8.3 - For Problems, 17-32, determine the general...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problem 33-37, solve the given initial value...Ch. 8.3 - For Problem 33-37, solve the given initial value...Ch. 8.3 - For Problems 33-37, solve the given initial value...Ch. 8.3 - For Problems 33-37, solve the given initial value...Ch. 8.3 - For Problems 33-37, solve the given initial value...Ch. 8.3 - At time t the displacement from equilibrium, y(t),...Ch. 8.3 - For Problems 39-47, determine an appropriate trial...Ch. 8.3 - For Problems 39-47, determine an appropriate trial...Ch. 8.3 - For Problems 39-47, determine an appropriate trial...Ch. 8.3 - For Problems 39-47, determine an appropriate trial...Ch. 8.3 - For Problems 39-47, determine an appropriate trial...Ch. 8.3 - Problems For problems 39-47, determine an...Ch. 8.3 - Prob. 45PCh. 8.3 - Problems For problems 39-47, determine an...Ch. 8.3 - Problems For problems 39-47, determine an...Ch. 8.3 - Problems Derive an appropriate trial solution for...Ch. 8.5 - For Questions ai, decide if the given statement is...Ch. 8.5 - For Questions ai, decide if the given statement is...Ch. 8.5 - For Questions ai, decide if the given statement is...Ch. 8.5 - Prob. 4TFRCh. 8.5 - For Questions ai, decide if the given statement is...Ch. 8.5 - Prob. 6TFRCh. 8.5 - Prob. 7TFRCh. 8.5 - Prob. 8TFRCh. 8.5 - Prob. 9TFRCh. 8.5 - Prob. 1PCh. 8.5 - Prob. 2PCh. 8.5 - A force of 3N stretches a spring by 1m. a Find the...Ch. 8.5 - For Problems 4-10, determine the motion of the...Ch. 8.5 - For Problems 4-10, determine the motion of the...Ch. 8.5 - For Problems 4-10, determine the motion of the...Ch. 8.5 - For Problems 4-10, determine the motion of the...Ch. 8.5 - For Problems 4-10, determine the motion of the...Ch. 8.5 - For Problems 4-10, determine the motion of the...Ch. 8.5 - Prob. 10PCh. 8.5 - In the previous problem, find the time at which...Ch. 8.5 - Consider the spring-mass system whose motion is...Ch. 8.5 - Consider the spring-mass system whose motion is...Ch. 8.5 - Consider the spring-mass system whose motion is...Ch. 8.5 - Prob. 15PCh. 8.5 - Prob. 16PCh. 8.5 - Prob. 18PCh. 8.5 - Prob. 19PCh. 8.5 - Prob. 20PCh. 8.5 - Prob. 21PCh. 8.5 - An object of mass m is attached to the midpoint of...Ch. 8.5 - Repeat the previous problem if the string has...Ch. 8.5 - Consider the damped spring-mass system whose...Ch. 8.5 - Consider the spring-mass system whose motion is...Ch. 8.5 - Consider the spring-mass system whose motion is...Ch. 8.5 - Prob. 27PCh. 8.5 - The general solution of forced undamped...Ch. 8.5 - Determine the period of the motion for the...Ch. 8.5 - Prob. 30PCh. 8.5 - Prob. 31PCh. 8.5 - Consider the damped spring-mass system with m=1,...Ch. 8.5 - Consider the spring-mass system whose motion is...Ch. 8.5 - Prob. 34PCh. 8.6 - For Questions af, decide if the given statement is...Ch. 8.6 - Prob. 2TFRCh. 8.6 - Prob. 3TFRCh. 8.6 - For Questions af, decide if the given statement is...Ch. 8.6 - Prob. 5TFRCh. 8.6 - Prob. 6TFRCh. 8.6 - Problems Determine the charge on the capacitor at...Ch. 8.6 - Problems Determine the steady current in the RLC...Ch. 8.6 - Prob. 3PCh. 8.6 - Prob. 4PCh. 8.6 - Consider the RLC circuit with R=16, L=8H, C=140F,...Ch. 8.6 - Show that the differential equation governing the...Ch. 8.6 - Prob. 7PCh. 8.6 - Prob. 8PCh. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the...Ch. 8.7 - Problems For Problems 122, use the...Ch. 8.7 - Problems For Problems 122, use the...Ch. 8.7 - Prob. 12PCh. 8.7 - Prob. 13PCh. 8.7 - Problems For Problems 122, use the...Ch. 8.7 - Problems
For Problems 1-22, use the...Ch. 8.7 - Problems
For Problems 1-22, use the...Ch. 8.7 - Prob. 17PCh. 8.7 - Prob. 18PCh. 8.7 - Prob. 19PCh. 8.7 - Prob. 20PCh. 8.7 - Prob. 21PCh. 8.7 - Prob. 22PCh. 8.7 - Problems
For Problems 23-26, use a Greens...Ch. 8.7 - Problems
For Problems 23-26, use a Greens...Ch. 8.7 - Problems For problems 23-26, use a Greens function...Ch. 8.7 - Problems For problems 23-26, use a Greens function...Ch. 8.7 - Problems For problem 27-28, use a Greens function...Ch. 8.7 - Prob. 28PCh. 8.7 - Prob. 29PCh. 8.7 - Problems Consider the differential equation...Ch. 8.7 - Prob. 31PCh. 8.7 - Prob. 32PCh. 8.7 - Prob. 33PCh. 8.7 - Prob. 34PCh. 8.7 - Prob. 35PCh. 8.7 - Prob. 36PCh. 8.7 - Prob. 37PCh. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 9-11, find the solution to...Ch. 8.8 - Prob. 10PCh. 8.8 - Prob. 11PCh. 8.8 - Problems
Consider the Cauchy-Euler equation
...Ch. 8.8 - Problems
For Problems 14-21, solve the given...Ch. 8.8 - Problems
For Problems 14-21, solve the given...Ch. 8.8 - Problems
For Problems 14-21, solve the given...Ch. 8.8 - Problems
For Problems 14-21, solve the given...Ch. 8.8 - Prob. 18PCh. 8.8 - Problems
For Problems 14-21, solve the given...Ch. 8.8 - Prob. 20PCh. 8.8 - Prob. 21PCh. 8.8 - Prob. 24PCh. 8.9 - For Problems 16, y1 is a solution to the given...Ch. 8.9 - For Problems 16, y1 is a solution to the given...Ch. 8.9 - For Problems 16, y1 is a solution to the given...Ch. 8.9 - For Problems 16, y1 is a solution to the given...Ch. 8.9 - For Problems 16, y1 is a solution to the given...Ch. 8.9 - For Problems 16, y1 is a solution to the given...Ch. 8.9 - Consider the Cauchy-Euler equation...Ch. 8.9 - Prob. 8PCh. 8.9 - Prob. 9PCh. 8.9 - For Problems 1015, y1 is a solution to the...Ch. 8.9 - For Problems 1015, y1 is a solution to the...Ch. 8.9 - Prob. 12PCh. 8.9 - Prob. 13PCh. 8.9 - Prob. 14PCh. 8.9 - For Problems 1015, y1 is a solution to the...Ch. 8.9 - Consider the differential equation...Ch. 8.10 - In Problems 1-6, find Ly for the given...Ch. 8.10 - Prob. 2APCh. 8.10 - Prob. 3APCh. 8.10 - Prob. 4APCh. 8.10 - Prob. 5APCh. 8.10 - Prob. 6APCh. 8.10 - Prob. 7APCh. 8.10 - Prob. 8APCh. 8.10 - Prob. 9APCh. 8.10 - Prob. 10APCh. 8.10 - Prob. 11APCh. 8.10 - Prob. 12APCh. 8.10 - Prob. 13APCh. 8.10 - In Problem 14-17, determine the annihilator of the...Ch. 8.10 - Prob. 15APCh. 8.10 - Prob. 16APCh. 8.10 - Prob. 17APCh. 8.10 - Prob. 18APCh. 8.10 - In Problem 18-23, determine a trial solution for...Ch. 8.10 - Prob. 20APCh. 8.10 - Prob. 21APCh. 8.10 - Prob. 22APCh. 8.10 - Prob. 23APCh. 8.10 - For Problems 24-29, solve the given nonhomogeneous...Ch. 8.10 - Prob. 25APCh. 8.10 - For Problems 24-29, solve the given nonhomogeneous...Ch. 8.10 - Prob. 27APCh. 8.10 - Prob. 28APCh. 8.10 - Prob. 29APCh. 8.10 - Prob. 30APCh. 8.10 - Prob. 31APCh. 8.10 - Prob. 32APCh. 8.10 - For Problem 30-39, state whether the annihilator...Ch. 8.10 - Prob. 34APCh. 8.10 - For Problem 30-39, state whether the annihilator...Ch. 8.10 - For Problem 30-39, state whether the annihilator...Ch. 8.10 - Prob. 37APCh. 8.10 - Prob. 38APCh. 8.10 - For Problem 30-39, state whether the annihilator...Ch. 8.10 - Prob. 40APCh. 8.10 - For Problems 40-45, use the annihilator to solve...Ch. 8.10 - Prob. 42APCh. 8.10 - Prob. 43APCh. 8.10 - Prob. 44APCh. 8.10 - Prob. 45APCh. 8.10 - Prob. 46APCh. 8.10 - Prob. 47APCh. 8.10 - For Problem 47-51, use the variations of...Ch. 8.10 - Prob. 49APCh. 8.10 - Prob. 50APCh. 8.10 - Prob. 51APCh. 8.10 - Prob. 52APCh. 8.10 - Prob. 53APCh. 8.10 - In the Problem 53-58, find the general solution to...Ch. 8.10 - Prob. 55APCh. 8.10 - In the Problem 53-58, find the general solution to...Ch. 8.10 - Prob. 57APCh. 8.10 - Prob. 58APCh. 8.10 - For Problems 59-61, solve the differential...Ch. 8.10 - Prob. 60APCh. 8.10 - Prob. 61APCh. 8.10 - Prob. 62APCh. 8.10 - Prob. 63APCh. 8.10 - Prob. 64APCh. 8.10 - Prob. 65APCh. 8.10 - Prob. 66AP
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- The Colossus Ferris wheel debuted at the 1984 New Orleans World's Fair. The ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The height above ground, h, of a passenger on the ride is a periodic function of time, t. The graph displays the height above ground of the last passenger to board over the course of the 15 min ride. Height of Passenger in Ferris Wheel 180 160 140- €120 Height, h (ft) 100 80 60 40 20 0 ך 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time of operation, t (min) Sine function model: h = −82.5 cos (3πt) + 97.5 where h is the height of the passenger above the ground measured in feet and t is the time of operation of the ride in minutes. What is the period of the sine function model? Interpret the period you found in the context of the operation of the Ferris wheel. Answer:arrow_forward1. Graph the function f(x)=sin(x) −2¸ Answer: y -2π 一元 1 −1 -2 -3 -4+ 元 2πarrow_forward3. Graph the function f(x) = −(x-2)²+4 Answer: f(x) 6 5 4 3 2+ 1 -6-5 -4-3-2-1 × 1 2 3 4 5 6 -1 -2+ ရာ -3+ -4+ -5 -6arrow_forward
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