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I saw the first one like this, but then I'm an engineer:
the work to compress any spring is 1/2K*(x^2)
where k is the spring constant.
So, you find the constant by backward calculating from your given, ie
54 = 1/2K (6^2)
therefore K = 54 (2) / 6^2
which equals 3.
Now plug that in for your new compression length, 12
W = 1/2 (3) (12^2)
= 216 in-lb
voila! No integrals needed!
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