This is to find constraint equations.

I explain it with the help of the following example:

 

 

Constraint equation would here give us the kinematic relation between the motions of the three masses.

You can get n constraint equation where n is the number of strings in the question.

Steps for making constraint equations

1.Mark a reference axis.

  Here let us take the axis as a line perpendicular to the strings passing to the topmost pulley.

2. Mark the distance of the every point from the axis where there is a moving body or there is a turn in the string.

Here as the axis passes thru the top pulley, its distance 4m the axis is 0.

Next let m1 be at x1, the second pulley at x4, m2 at x2, m3 at x3.

3. Calculate the lengths of the strings in terms of the assigned coordinates.

  Here,

 length of first string is  x1 + x4 = l1

and of second  (x3-x4) + (x2 - x4) = l2

4. Next is differentiating them to get the required relations...

   When u differentiate as the string is inextensible, l1 is constant, RHS becomes 0.

Now wen u differentiate somethin, you get the acceleration of the body dat was assigned that co-ordinate.

For instance, differentiating x1 wrt t once gives u velocity of m1 and twice, acc of m1.

I guess now u can form the relations.....