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For the arrangement shown, a cylinder of mass m with cross-sectional area A, initially in equilibrium poisition, is displaced slightly inside the liquid of density p. Prove that the motion is simple harmonic and also find its time-period. |
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Answer» Solution : `T=kx_(0)` and `T+Vrhog=mg` `rArr kx_(0)+Vrhog=mg` when `m` is displaced by `DELTAX` downwards `ma=T'-k(x_(0)+Deltax)` `rArr ma=mg-(v+Adeltax)rhog-T'` Adding `2ma=mg-k(x_(0)+Deltax)-(v+ADeltax)rhog` `=-[k+Arhog]Deltax`, using equation (`3`) `rArr a=-([k+Arhog])/(2m)Deltax` `:. T=(2PI)/(OMEGA)=2pisqrt((2m)/([k+Arhog]))` 
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