When two springs (each having stiffness constant K) are connected in series, the equivalent stiffness will be

Explanation:

In mechanics, two or more springs are said to be in series when they are connected end-to-end, and in parallel when they are connected side-by-side. 

Equivalent spring constant

In Series connection:

\(\frac{1}{{{k_{eq}}}} = \frac{1}{{{k_1}}} + \frac{1}{{{k_2}}}\)

\({k_{eq}} = \frac{{{k_1} \times {k_2}}}{{{k_1} + {k_2}}}\)

Here, k₁ = k₂ = k

\(\therefore {k_{eq}} = \frac{{{k_1} \times {k_2}}}{{{k_1} + {k_2}}}=\frac{{{k} \times {k}}}{{{k} + {k}}}=\frac{k^2}{2k}=\frac k2\)

Additional InformationIn Parallel connection:

\({k_{eq}} = {k_1} + {k_2}\)