1. A mass of 1 slug, when attached to a spring, stretches it 2feet and then comes to rest in the equilibrium position. Startingat t = 0, an external force equal to f(t) = 10 sin 4t is applied tothe system. Find the equation of motion if the surrounding mediumoffers a damping force that is numerically equal to 8 times theinstantaneous velocity. (Use g = 32 ft/s2 for the acceleration dueto gravity.)

2. A 1-kilogram mass is attached to a spring whose constant is18 N/m, and the entire system is then submerged in a liquid thatimparts a damping force numerically equal to 11 times theinstantaneous velocity. Determine the equations of motion if thefollowing is true.

(a) the mass is initially released from rest from a point 1meter below the equilibrium position

(b) the mass is initially released from a point 1 meter belowthe equilibrium position with an upward velocity of 11 m/s

3. A mass weighing 32 pounds stretches a spring 2 feet.

(a) Determine the amplitude and period of motion if the mass isinitially released from a point 1 foot above the equilibriumposition with an upward velocity of 6 ft/s.

(b) How many complete cycles will the mass have completed at theend of 6?seconds?

4. A force of 960 newtons stretches a spring 4 meters. A mass of60 kilograms is attached to the end of the spring and is initiallyreleased from the equilibrium position with an upward velocity of10 m/s. Find the equation of motion.