How will you calculate the length of the S period.

Explanation

According to Newton.s second law
`F= (dp)/(dt) ` i.e. `dp = F dt`
Integrate it over a time interval from `t_1 ` to `t_f`
`int_i^f dp = int_(t_1)^(t_f)F dt`
`P_f - P_i = int_(t_1)^(t_2) F. dt`
`P_1 to` initial momentum of the object at `t_1`
`P_f to ` Final momentum of the object at `t_f`
`P_f - P_i = Deltap=` change in momentum during the time interval `Deltat. int_(t_1)^(t_f) F dt` = J is called the impulse.
If the force is constant over the time interval `Deltat`, then
`int_(t_1)^(t_f) F dt = F int_(t_1)^(t_f) dt = F(t_f - t_i) = F Deltat`
`J = F Deltat= Deltap`
Hence the proof.