# Problem on springs [closed]

(ans: D) I have tried the problem by finding relation between extensions of the springs which comes out to be F/3k for the upper and lower spring and 2F/3k for the middle two. And then i get stuck as i dont know how to proceed further

• Can you show us your free body diagrams? – Chris K8NVH Jul 31 '19 at 13:22
• This problem can be simplified by capitalizing on the symmetry of the system. If we situate an observer at the center of the middle string (half-way between the two pulleys), then, relative to this observer, the attachment at the wall moves to the left by a displacement x and the block moves to the right with an equal displacement x; and the point on string where the observer is situated does not move at all. If the upper pulley moves to the right by a displacement y, the upper spring increases in length by y+x. And the spring between the upper pulley and the block increases by x-y. – Chet Miller Jul 31 '19 at 16:07
• @ChetMiller I think the upper spring actually increases in length by $2y+x$ because the total length of the upper and lower springs and the strings wrapped around the pulleys increases by $4y+2x$. – gandalf61 Jul 31 '19 at 16:25
• @gandalf61 If the upper pulley moves to the right by a displacement y (relative to an observer situated at the center of the middle string), the right end of the upper spring moves to the right by an equal amount (because the point at the middle of the center string does not move in this moving frame of reference). And we already said that the left end of the upper spring moves to the left a displacement x (in this frame of reference). – Chet Miller Jul 31 '19 at 16:39
• @ChetMiller Think about the distance following the string and spring between the middle observer and the wall (or, equivalently, between the middle observer and the block). This distance changes by $2y+x$, which must equal the extension of the upper spring. – gandalf61 Jul 31 '19 at 16:44