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A force of 9 N stretches a spring 1 m. A mass weighing 1.96 N is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 1.2 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 m above the equilibrium position. -3 x(t)e -cos 6-0.5 sin 6r m (b) Express the equation of motion in the form x Aet sin(√er² - 2²t + a), which is given in (23) of Section 3.8. (Round to two decimal places.) x(t)=1.12e sin 6+1.11 m

A force of 9 N stretches a spring 1 m. A mass weighing 1.96 N is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 1.2 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 m above the equilibrium position. -3 x(t)e -cos 6-0.5 sin 6r m (b) Express the equation of motion in the form x Aet sin(√er² - 2²t + a), which is given in (23) of Section 3.8. (Round to two decimal places.) x(t)=1.12e sin 6+1.11 m

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 9 N stretches a spring 1 m. A mass weighing 1.96 N is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 1.2 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 m above the equilibrium position. -3 x(t)e -cos 6-0.5 sin 6 (b) Express the equation of motion in the form x(1) Aeon (√²-2²t+o). which is given in (23) of Section 3.8. (Round to two decimal places.) x(t) 1.12e sin 6+1.11 Minik x m m (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.) 0.863
Transcribed Image Text:A force of 9 N stretches a spring 1 m. A mass weighing 1.96 N is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 1.2 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 m above the equilibrium position. -3 x(t)e -cos 6-0.5 sin 6 (b) Express the equation of motion in the form x(1) Aeon (√²-2²t+o). which is given in (23) of Section 3.8. (Round to two decimal places.) x(t) 1.12e sin 6+1.11 Minik x m m (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.) 0.863
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