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A force of 9 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds 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 foot above the equilibrium position. x(t) = ft (b) Express the equation of motion in the form x(t) = Ae-at x(t) = * sin(√w² - 2²t + 4), , which is given in (23) of Section 3.8. (Round p to two decimal places.) ft (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.) S

A force of 9 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds 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 foot above the equilibrium position. x(t) = ft (b) Express the equation of motion in the form x(t) = Ae-at x(t) = * sin(√w² - 2²t + 4), , which is given in (23) of Section 3.8. (Round p to two decimal places.) ft (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.) S

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A force of 9 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds 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 foot above the equilibrium position. ft x(t) = = -λt (b) Express the equation of motion in the form x(t) = Ae¯ sin(√²-2²t+ x(t) = = ft q²t + 9), which is given in (23) of Section 3.8. (Round p to two decimal places.) (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.) S
Transcribed Image Text:A force of 9 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds 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 foot above the equilibrium position. ft x(t) = = -λt (b) Express the equation of motion in the form x(t) = Ae¯ sin(√²-2²t+ x(t) = = ft q²t + 9), which is given in (23) of Section 3.8. (Round p to two decimal places.) (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.) S
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