After a mass weighing 10 pounds is attached to a 5-foot spring, the spring measures 7 feet. This mass is removed and replaced with another mass that weighs 8 pounds. The entire system is placed in a medium that offers a damping force numerically equal to the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from a point 1 2 foot below the equilibrium position with a downward velocity of 1 ft/s. (b) Express the equation of motion in the form given in (23). (c) Find the times at which the mass passes through the equilibrium position heading downward. (d) Graph the equation of motion.
After a mass weighing 10 pounds is attached to a 5-foot spring, the spring measures 7 feet. This mass is removed and replaced with another mass that weighs 8 pounds. The entire system is placed in a medium that offers a damping force numerically equal to the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from a point 1 2 foot below the equilibrium position with a downward velocity of 1 ft/s. (b) Express the equation of motion in the form given in (23). (c) Find the times at which the mass passes through the equilibrium position heading downward. (d) Graph the equation of motion.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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After a mass weighing 10 pounds is attached to a 5-foot spring,
the spring measures 7 feet. This mass is removed and replaced
with another mass that weighs 8 pounds. The entire system is
placed in a medium that offers a damping force numerically
equal to the instantaneous velocity.
(a) Find the equation of motion if the mass is initially released
from a point 1
2 foot below the equilibrium position with
a downward velocity of 1 ft/s.
(b) Express the equation of motion in the form given
in (23).
(c) Find the times at which the mass passes through the equilibrium position heading downward.
(d) Graph the equation of motion.
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