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.

Explanation

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)`