Two springs having spring constants k_1 and k | vedclass

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(A) For parallel connection,the equivalent spring constant is $k_p = k_1 + k_2 = 9 \dots (1)$For series connection,the equivalent spring constant is $

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$6 	ext{ unit}, 3 	ext{ unit}$

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(A) For parallel connection,the equivalent spring constant is $k_p = k_1 + k_2 = 9 \dots (1)$For series connection,the equivalent spring constant is $k_s = \frac{k_1 k_2}{k_1 + k_2} = 2 \dots (2)$Substituting equation $(1)$ into equation $(2)$:$\frac{k_1 k_2}{9} = 2 \implies k_1 k_2 = 18 \dots (3)$From $(1)$,$k_2 = 9 - k_1$. Substituting this into $(3)$:$k_1(9 - k_1) = 18$$9k_1 - k_1^2 = 18$$k_1^2 - 9k_1 + 18 = 0$Factoring the quadratic equation:$(k_1 - 6)(k_1 - 3) = 0$Thus,$k_1 = 6 	ext{ unit}$ or $k_1 = 3 	ext{ unit}$.If $k_1 = 6$,then $k_2 = 3$. If $k_1 = 3$,then $k_2 = 6$.Therefore,the values are $6 	ext{ unit}$ and $3 	ext{ unit}$.

Two springs having spring constants $k_1$ and $k_2$ are connected in series,their resultant spring constant is $2 \text{ unit}$. If they are connected in parallel,their resultant spring constant is $9 \text{ unit}$. Find the values of $k_1$ and $k_2$.

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