Answered: A 6-foot spring measures 7 feet long…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A 6-foot spring measures 7 feet long after a mass weighing 4 pounds is attached to it. The medium through which the
mass moves offers a damping force numerically equivalent to 2 times the instantaneous velocity.
(a) Find the equation of motion if the mass is initially released from the equilibrium position with an upward
velocity of 4 ft/s. (Use the convention that displacements measured below the equilibrium position are positive).

y = ((2-sqrt(2))/2)e^{4(sqrt(2)-2)x}-(2-sqrt(2)/2)e^{-4(2+sqrt(2))x}

(b) What type of motion does the solution of the initial value problem describe? (free undamped (simple harmonic)
motion, free overdamped motion, free critically damped motion, or free underdamped (oscillatory) motion)

Free overdamped

1. A 6-foot spring measures 7 feet long after a mass weighing 4 pounds is attached to it. The medium through which the
mass moves offers a damping force numerically cquivalent to 2 times the instantancous velocity.
(a) Find the cquation of motion if the mass is initially relcased from the cquilibrium position with an upward
velocity of 4 ft/s. (Use the convention that displacements measured below the cquilibrium position are positive).
-(2 -Va le
e 4(2+ra) x
(b) What type of motion does the solution of the initial value problem describe? (free undamped (simple harmonic)
motion, free overdamped motion, free critically damped motion, or free underdamped (oscillatory) motion)
free
overdamped

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