466_Physics ProblemsTechnical Physics

466_Physics ProblemsTechnical Physics - 468 P15.71...

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468 Oscillatory Motion P15.71 (a) When the mass is displaced a distance x from equilibrium, spring 1 is stretched a distance x 1 and spring 2 is stretched a distance x 2 . By Newton’s third law, we expect kx 11 22 = . When this is combined with the requirement that xx x =+ 12 , FIG. P15.71 we find x k kk x 1 2 = + L N M O Q P The force on either spring is given by F xm a 1 = + L N M O Q P = where a is the acceleration of the mass m . This is in the form Fkxm a eff == and T m k mk k eff + ππ bg (b) In this case each spring is distorted by the distance x which the mass is displaced. Therefore, the restoring force is Fk k x =− + and k eff so that T m = + 2 π . P15.72 Let A represent the length below water at equilibrium and
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