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A force of 2 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 0.8 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) =-e-4¹ (cos(2t) + 2 sin(2t)) ft (b) Express the equation of motion in the form x(t) = Aeit sin(√w² - 1²t + p), which is given in (23) of Section 3.8. (Round to two decimal places.) ft

A force of 2 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 0.8 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) =-e-4¹ (cos(2t) + 2 sin(2t)) ft (b) Express the equation of motion in the form x(t) = Aeit sin(√w² - 1²t + p), which is given in (23) of Section 3.8. (Round to two decimal places.) ft

Advanced Engineering Mathematics
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 force of 2 pounds stretches a spring 1 foot. 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 0.8 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) = -e 4t(cos(2t) + 2 sin(2t)) (b) Express the equation f motion in the form x(t) = Ae-it sin(√²-2²t+4), which is given in (23) of Section 3.8. (Round p to two decimal places.) x(t) = ft Read It ft (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.) 2.910 ✔S Need Help? Watch It
Transcribed Image Text:A force of 2 pounds stretches a spring 1 foot. 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 0.8 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) = -e 4t(cos(2t) + 2 sin(2t)) (b) Express the equation f motion in the form x(t) = Ae-it sin(√²-2²t+4), which is given in (23) of Section 3.8. (Round p to two decimal places.) x(t) = ft Read It ft (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.) 2.910 ✔S Need Help? Watch It
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