Question

(7 points) 14. A mass weighing 4 pounds stretches a spring 2 feet. The system is submerged in a medium which offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 8 ft/s. Find the equation of motion, ä(t). What type of damped motion is this system?

Answer 1

Consider, a mass mw weighting mo aft at eqbm. pounds streches a streches a spring buy 4 theo 4 lbs 9 = 32 34620/62 .' m = 1 2 se -tlg lbs. AL- ft.

The cond ?? ?? of eab? net Porce on here, acting forces - system = 0. ТКА. mg ma i) restoring force to = kal(upcourtd.) üy weight W= ( downward) sos (restoring force) - (weight)

KAL 4 / Fr=-ka mg k: = 2 lb/ft In case of given motion for ce acting of i) restoring force, ny frictional force. If -bai So, by Newton's and law of motim, Wa E-ka-bà

I äta + 2a=0 8 a + 8 8 + 1690 the mass initially released from alo) = f ft with down world velocity vio) = -84445. sign due to down word . - set of equ teque of motim ä+ 8 x+16x = 0 200) = 1 ift á (0) = - -8f615. initiah ondan mät bätka = 0 2) ä+a8a+w.hx=0 b theres se Nol = km am putting numerical values Pozidla: 4 4. We 2 4 //M here, 8 = wo Samped in nature eritically So, motion a cri