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. Find the equation of motion If the mass is initially released from rest from a point 1 foot above the equilibrium position.

Explanation:

let be the mass attached, let be the spring constant and let be the positive damping constant.

-By Newton's second law:

where is the displacement from equilibrium position. The equation can be transformed into:

 shich is the equation of motion.

from

explanation:

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