Let `v_(0)` be the spee do fhte ball just before first collisiion and `v_(1)` be the speed just after first collision.
From the definition of the coefficient of restitution.
`v_(1)=ev_(0)`………..i
Just before second collision seed of the ball will be `v_(1)` only. if `v_(2)` be the speed just after second collision then
`v_(2)=ev_(1)=e^(2)v_(0)`...............ii
Similarly `V_(n)=e^(n)v0`..............iii
If after `nth` collisionmaximum deflection of the strig from veritcal is `theta` then from COE, we get
`=1/2mv_(n)^(2)=mg(1-costheta)`
`implies e^(2n)v_(0)^(2)=2gl(1-costheta)`.........iv
also from COE `v_(0)^(2)=2gl....................v`
frm iv and `v` we get `theta=cos^(-1)(1-e^(2n))`