456_Physics ProblemsTechnical Physics

456_Physics ProblemsTechnical Physics - 458 Oscillatory...

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458 Oscillatory Motion (b) The energy of the m 1 -spring system at equilibrium is: 1 2 1 2 9 00 0 500 1125 1 2 2 mv == .. . kg m s J bg b g . This is also equal to 1 2 2 kA af , where A is the amplitude of the m 1 -spring system. Therefore, 1 2 100 2 a f = A . or ′= A 0150 . m . The period of the m 1 -spring system is T m k 21 8 8 5 1 π s and it takes 1 4 0471 T = . s after it passes the equilibrium point for the spring to become fully stretched the first time. The distance separating m 1 and m 2 at this time is: Dv T A = F H G I K J −′ = = = 4 0 500 0 471 0 150 0 085 6 8 56 . . . ms s m cm . P15.53 dx dt A 2 2 2 F H G I K J = max ω f n mg mA A g ss s max . = µµ µ 2 2 662±cm f n m g B P B s FIG. P15.53 P15.54 The maximum acceleration of the oscillating system is aA A f max ωπ 22 2 4 . The friction force exerted between the two blocks must be capable of accelerating block B at this rate. Thus, if Block
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