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At the moment t=0 a particle of mass m starts moving due to a force F=F_0 sin omega t, where F_0 and omega are constants. Find the distance covered by the particle as a function of t. Draw the approximate plot of this function. |
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Answer» Solution :We have `F=F_0sin omegat` or `m(dvecv)/(dt)=vecF_0sin omegat` or `md vecv=vecF_0sin omegat dt` On INTEGRATING, `vecmv=(-vecF_0)/(omega)cos omegat+C`, (where C is integration CONSTANT) When `t=0`, `v=0`, so `C=(vecF_0)/(momega)` Hence, `vecv=(-vecF_0)/(momega)cos omegat+(vecF_0)/(momega)` As `|cos omegatle1` so, `v=(F_0)/(momega)(1-cos omegat)` THUS `s=underset(0)overset(t)int v dt` `=(F_0t)/(momega)-(F_0sin omegat)/(momega^2)=(F_0)/(momega^2)(omegat-sinomegat)` |
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