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**

- Nothing bad happens to Adarsh.
- Consider Adarsh to be a point sized particle.

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