Answered: (a) Write the second-order linear… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 18EQ

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4. A 1 kg mass is attached to a spring whose constant is 6 N/m, and the entire system is submerged in a liquid that
imparts a damping force equal to 2 times the instantaneous velocity.

(a) Write the second-order linear differential equation to model the motion.
(b) Convert the second-order linear differential equation from part (a) to a first-order linear system.
(c) Classify the critical (equilibrium) point (0,0).

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Suppose it takes 4 pounds of force to keep a spring stretched 3 inches longer than its equilibrium length. How much work does it take to stretch this same spring from its equilibrium length to one foot longer than its equilibrium length?
A mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 16 ft/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Useg = 32 ft/s? for the acceleration due to gravity.) Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position. What is the position (in ft) of the mass at this instant? ft
A mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 16 ft/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Use g = 32 ft/s? for the acceleration due to gravity.) Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position. What is the position (in ft) of the mass at this instant? ft

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