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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 1 125 1 2 2 m v = = . . . kg m s J b gb g . This is also equal to 1 2 2 k A a f , where A is the amplitude of the m 1 -spring system. Therefore, 1 2 100 1 125 2 a fa f = A . or ′ = A 0 150 . m. The period of the m 1 -spring system is T m k = = 2 1 885 1 π . s and it takes 1 4 0 471 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: D v T A = F H G I K J ′ = = = 4 0 500 0 471 0 150 0 085 6 8 56 . . . . . m s s m cm a f . P15.53 d x dt A 2 2 2 F H G I K J = max ω f n mg mA A g s s s max . = = = = = µ µ ω µ ω 2 2 6 62 cm f n m g B P B µ s FIG. P15.53 P15.54 The maximum acceleration of the oscillating system is a A Af max = = ω π 2 2 2 4 . The friction force
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