Tight-Slack-Tight-Slack-Tight-Slack-Tight-Slack...

A block is tied to a fixed support using a light string of length $\sqrt { 2 } m$ . It is given a velocity $(\sqrt { 2 } +1)\sqrt { g }$ from the lowermost position. At point A the string becomes slack and the block moves as projectile in a parabolic path. The string again becomes tight at point B whose coordinates are given by (a,b) if the rigid support is taken as origin. Find ${ a }^{ 4 }+{ b }^{ 4 }+6{ a }^{ 2 }{ b }^{ 2 }+4a{ b }^{ 2 }$

This problem is originally part of set Mechanics problems by Abhishek Sharma .

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