458 Oscillatory Motion(b)The energy of the m1-spring system at equilibrium is:12129 000 5001 125122m v==...kgmsJbgbg.This is also equal to 122k A′a f, where ′Ais the amplitude of the m1-spring system.Therefore,121001 1252afa f′=A.or ′ =A0 150.m.The period of the m1-spring system is Tmk==21 8851π.sand it takes 140 471T=.s after it passes the equilibrium point for the spring to become fullystretched the first time. The distance separating m1and m2at this time is:DvTA=FHGIKJ−′ =−==40 5000 4710 1500 085 68 56.....mssmcmaf.P15.53d xdtA222FHGIKJ=maxωfnmgmAAgsssmax.=====µµωµω226 62 cmfnmgBPBµsFIG. P15.53P15.54The maximum acceleration of the oscillating system is aAAfmax==ωπ2224. The friction force
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