Answer
We can rank the arrangements according to the work done on the block by the spring forces, from largest to smallest:
$(1) \gt (2) \gt (3)$
Work Step by Step
Let $k$ be the spring constant of each spring.
Arrangement (1):
If the block is displaced by a distance $d$ to the left, the two springs are compressed by a distance $d$. The work done on the block by each spring is $-\frac{1}{2}kd^2$. The work done on the block by the spring forces is $-kd^2$
Arrangement (2):
If the block is displaced by a distance $d$ to the left, the two springs on the left are compressed by a distance $d$. The spring on the right is stretched by a distance $d$. The work done on the block by each spring is $-\frac{1}{2}kd^2$. The work done on the block by the spring forces is $-\frac{3}{2}kd^2$
Arrangement (3):
If the block is displaced by a distance $d$ to the left, the two springs on the left are compressed by a distance $d$. The two springs on the right are stretched by a distance $d$. The work done on the block by each spring is $-\frac{1}{2}kd^2$. The work done on the block by the spring forces is $-2kd^2$
We can rank the arrangements according to the work done on the block by the spring forces, from largest to smallest:
$(1) \gt (2) \gt (3)$
