A mass weighing 8 pounds is attached to a spring whose constant is 4 lb/ft. The medium offers adamping force that is numerically equal to the two times instantaneous velocity. The mass is initiallyreleased from a point 1 foot above the equilibrium position with a downward velocity of 8 ft/s.(a) Specify the 2nd order DE as an IVP for the mass spring system.(b) Solve the equation to find the position of the mass at any time t.(c) Determine the time at which the mass passes through the equilibrium position.(d) Find the time at which the mass attains its extreme displacement from the equilibrium position. Whatis the position of the mass at this instant? 5. A mass weighing 8 pounds is attached to a spring whose constant is 4 lb/ft. The medium offers adamping force that is numerically equal to the two times instantaneous velocity. The mass is initiallyreleased from a point 1 foot above the equilibrium position with a downward velocity of 8 ft/s.(a) Specify the 2"nd order DE as an IVP for the mass spring system.(b) Solve the equation to find the position of the mass at any time t.(c) Determine the time at which the mass passes through the equilibrium position.(d) Find the time at which the mass attains its extreme displacement from the equilibrium position. Whatis the position of the mass at this instant?

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Answered: A mass weighing 8 pounds is attached to…

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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A mass weighing 8 pounds is attached to a spring whose constant is 4 lb/ft. The medium offers a
damping force that is numerically equal to the two times instantaneous velocity. The mass is initially
released from a point 1 foot above the equilibrium position with a downward velocity of 8 ft/s.
(a) Specify the 2nd order DE as an IVP for the mass spring system.
(b) Solve the equation to find the position of the mass at any time t.
(c) Determine the time at which the mass passes through the equilibrium position.
(d) Find the time at which the mass attains its extreme displacement from the equilibrium position. What
is the position of the mass at this instant?

5. A mass weighing 8 pounds is attached to a spring whose constant is 4 lb/ft. The medium offers a
damping force that is numerically equal to the two times instantaneous velocity. The mass is initially
released from a point 1 foot above the equilibrium position with a downward velocity of 8 ft/s.
(a) Specify the 2"nd order DE as an IVP for the mass spring system.
(b) Solve the equation to find the position of the mass at any time t.
(c) Determine the time at which the mass passes through the equilibrium position.
(d) Find the time at which the mass attains its extreme displacement from the equilibrium position. What
is the position of the mass at this instant?

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