Two springs having spring constant `k_(1)" and "k_(2)` is connected in series, its resultant spring constant will be 2 unit. Now if they connected in parallel its resultants spring constant will be 9 unit, then find the value of `k_(1)" and "k_(2)`.

Explanation

For parallel connection `k_(1)+ k_(2)= 9" ""……"(1)`
For series connection `(k_(1)k_(2))/(k_(1)+k_(2))=2 " ""………"(2)`
From equation (1) and (2) `=(k_(1)k_(2))/(9)`
`therefore k_(1)+k_(2)= 18 " ""…….."(3)`
`therefore k_(2) = (18)/(k_1)` putting in equation (1)
`k_(1)= (18)/(k_1)=9`
`therefore k_(1)^(2) +18"" 9k_(1)`
`therefore k_(1)^(2) - 9k_(1)+18=0`
`therefore (k_(1)-6)(k_(1)-3)=0`
`therefore k_(1)= 6" unit or "k_(1)= 3` unit
`therefore k_(2)= 3 " unit or "k_(2) = 6` unit.