• # question_answer A flat plate P of mass 'M? executes SHM in a horizontal plane by sliding over a frictionless surface with a frequency V. A block 'B' of mass 'm' rests on the plate as shown in figure. Coefficient of friction between the surface of B and P  , is a. What is the maximum amplitude of oscillation that the plate block system can have if the block B is not to slip on the plate: A)  $\frac{\mu g}{4{{\pi }^{2}}{{V}^{2}}}$                 B)  $\frac{\mu g}{4{{\pi }^{2}}V}$C)  $\frac{\mu }{4{{\pi }^{2}}{{V}^{2}}g}$                     D)  $\frac{\mu }{2{{\pi }^{2}}{{V}^{2}}}$

Solution :

${{f}_{\max }}=\mu mg,\,{{a}_{\max }}=\mu g.$ If A is the amplitude ${{a}_{\max }}=A{{\omega }^{2}}=4{{\pi }^{2}}A{{V}^{2}}=\mu g$ Therefore,  $A=\frac{\mu g}{4{{\pi }^{2}}{{V}^{2}}}.$

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