The Work Done By The Spring Force .

"Here how did you get 3^2  ? it must be ( 5^2 - 3^2 ) according to ( Sf^2 - Si^2 ) ! ​ "

Sf and Si are the distances from the unstretched position.  So Sf = 2-5 (i.e. 3)  and Si = 5-5 (i.e. 0)

Yes.

\(U_s=\int_{s_1}^{s_2}(-kx)dx \rightarrow U_s=-\frac{k}{2}(s_2^2-s_1^2)\)

So his answer is incorrect too right ? 

And please explain this question for me 

The work done on the spring to get it from 5" to 2" is k*3^2/2

The work done on the spring to get it from 5" to 4" is k*1^2/2

Hence the work done on the spring to get from 2" to 4" is k*(1^2 - 3^2)/2 or -k*(3^2 - 1^2)/2  (it's the work done by the spring that's positive here of course, so the work done on the spring is negative).

Thanks Alan :)

The work done on the spring to get it from 5" to 2" is k*3^2/2 

Here how did you get 3^2  ? it must be ( 5^2 - 3^2 ) according to ( Sf^2 - Si^2 ) ! 

Now I get it . 

Thank you Alan