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A spring of force constant k is cut into...

A spring of force constant k is cut into two pieces of lengths `l_(1)` and `l_(2).` Calculate force constant of each part.

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As for a spring, force constant `k prop (1//l)`
So, `k_(1) prop1/l_(1),k_(2)prop1/l_(2) and k prop1/(l_(1)+l_(2))`
So, `k_(1)/k=(l_(1)+l_(2))/l_(1) and k_(2)/k=(l_(1)+l_(2))/l_(2)`
i.e, `k_(1)=k(1+l_(2)/l_(1)) and k_(2)=k(1+l_(1)/l_(2))`
Note: if `l_(1):l_(2)::1:n,i.e.,l_(2)=nl_(1),k_(1)=k(1+n) and k_(2)=[1+(1//n)]k.`
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