Two identical springs of spring constant $k$ are connected in series. What is the effective spring constant $k_{\text{eff}}$ of the combination?

Solution

1. For two springs connected in series, the effective spring constant $k_{\text{eff}}$ is determined by the formula $\frac{1}{k_{\text{eff}}}=\frac{1}{k_1}+\frac{1}{k_2}$.
2. Given that both springs are identical with spring constant $$\begin{array}{rl}{k}_1& =k_2\\ & =k\end{array}$$, we substitute these values into the equation: $$\begin{array}{rl}\frac{1}{k_{\text{eff}}}& =\frac{1}{k}+\frac{1}{k}\\ & =\frac{2}{k}\end{array}$$.
3. Taking the reciprocal of both sides, we find the effective spring constant to be $k_{\text{eff}}=\frac{k}{2}$.
4. Hence the answer is (A).