# Simple isn't it? #6

A group of friends from BRILLIANT decide to go for a bungee jumping camp. The first one to jump is Adarsh. He jumps from the top of a cliff of height $$H$$. He performs a damped oscillatory motion along the vertical motion. The first time he reaches at the lowest level ,i.e, height of $$0\text{ m}$$ above the ground. Then he goes up to a certain height. Similar type of motion goes on until an equilibrium state is obtained at height $h=\frac{51H}{200}$.

Find the original length length of rope used for bungee jumping.

The length is of the form $$\frac{aH}{b}$$, where $$a$$ and $$b$$ are positive co-prime integers.

Find $$a+b$$

Details and Assumptions