Question

A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches thespring 112112 feet. The ball is started in motion from the equilibrium position with adownward velocity of 22 feet per second. The air resistance (in pounds) of themoving ball numerically equals 4 times its velocity (in feet per second).Let u(t)u(t) be the displacement of the mass from equilibrium. Suppose that after tseconds the ball is u feet below its rest position. Find u (in feet) in terms of t. (Notethat the positive direction is down.)Take as the gravitational acceleration 32 feet per second per second.U=u=How would you characterize the damping in this mass-spring system?​

Answer 1

Step-by-step explanation:

Question: A Hollow Steel Ball Weighing 4 Pounds Is Suspended From A Spring. This Stretches The Spring 1/8 Feet. The Ball Is Started In Motion From The Equilibrium Position With A Downward Velocity Of 6 Feet Per Second. The Air Resistance (In Pounds) Of The Moving Ball Numerically Equals 4 Times Its Velocity (In Feet Per Second) . Suppose That After T Seconds The Ball

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A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring 1/8 feet. The ball is started in motion from the equilibrium position with a downward velocity of 6 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t.

Take as the gravitational acceleration 32 feet per second per second. (Note that the positive y direction is down in this problem.)