Question

2. An 8 lb object stretches a spring 1/2 ft by itself when there is no damper attached. Then, a damper is attached to it that will exert a force of 12 lbs when the velocity is 2 ft/s. Is this system over- damped, under-damped, or critically damped? (6 points) a) b) Find the displacement at any time t, u(t). (6 points) c) Sketch of the displacement of the mass for the first 10 seconds. (4 points) d) Discuss the long-term behavior of the oscillating mass. (2 points)

Answer 1

whon rnai 2. 2fkm

Conside. the ualtatim % motrn using Newton's 2nd law. Calularte the lsplac anafomation Lalculata th bnvse laplace op above pquatio

(c)

Sketch the displacement of mass for first 10 seconds.

6 4 0 0246 4218642

(d)

Consider the behavior of system for long time.

15 0 42186420246

Above response shows that value of displacement is keep on decreasing and tends to zero after long time.