Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Question
Chapter 3.8, Problem 29E
(a)
To determine
The equation of motion when mass is released from rest from a given point.
(b)
To determine
The equation of motion in required form.
(c)
To determine
The time at which the mass passes through the equilibrium position.
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A force of 4 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 0.4 times the
instantaneous velocity.
(a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position.
x(t)
=
ft
(b) Express the equation of motion in the form x(t) = Ae-¹t sin(√w² - 2²t + p), which is given in (23) of Section 3.8. (Round up to two decimal places.)
x(t) =
ft
(c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.)
S
A force of 5 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force
numerically equal to 1.2 times the instantaneous velocity.
(a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position.
x(t) =
ft
(b) Express the equation of motion in the form x(t)
= Ae-At sin Vw2 – 2?t + p
P), which is given in (23) of Section 3.8. (Round o to two decimal places.)
x(t) =
ft
(c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.)
A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position.
(a) Find the position x of the mass at the times
t = ?/12, ?/8, ?/6, ?/4, and 9?/32 s.
(Use
g = 32 ft/s2
for the acceleration due to gravity.)
Chapter 3 Solutions
Advanced Engineering Mathematics
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