Find the constraint relation between a_(1),a_(2) "and" a_(3).

1.	Find the constraint relation between a_(1),a_(2) "and" a_(3).
Answer» Solution :Points 1,2,3 and 4 are movable . Let their dis-placements from a fixed line be` x_(1), x_(2) , x_(3) and x_(4)` We have `x_(1)+x_(4)=l_(1)`(LENGTH of first string )…(i) and` (x_(2)-x_(4))+(x_(3)-x_(4))=l_(2)` (length of second string) or `x_(2)+x_(3)-2x_(4)=l_(2)`...(ii) On double , DIFFERENTIATING with respect to time , we get `a_(1)+a_(4)=0`...(iii) and `a_(2)+a_(3)-2a_(4)=0`...(iv) But since `a_(4)=-a_(1) a_(4)=-a_(1)` [From equation (iii)] We have , a_(2)+a_(3)+2a_(1)=0` This is the required constraint RELATION between `a_(1),a_(2)" and " a_(3)`

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