A force of 13 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 1.6 times the instantaneousvelocity.(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-it sin v@² – 2²t + @ ), which is given in (23) of Section 3.8. (Round o to two decimal places.)x(t)ft(c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.)

Answered: uation of motion in the form x(t) =…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...

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A force of 13 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 1.6 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. (b) Express the equation of motion in the form (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.)
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uation of motion in the form x(t) = Ae™it sin( V2 – 2?t + w), which ft