A force of 5 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds is attached to the spring, and the system is then immersed in amedium 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.x(t) =(b) Express the equation of motion in the form x(t) } = Ae-¹t sin(√√w² - 2²t + $) which is given in (23) of Section 3.8. (Roundto two decimal places.)x(t) =ftftS(c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to threedecimal places.)

(a) Given values:The equation of motion can be expressed as: Simplifying, we get: The characteristic…

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