Two springs of constant ${k_1}$and ${k_2}$are joined in series. The effective spring constant of the combination is given by
AIPMT 2004, Easy
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(d)In series combination
$\frac{1}{{{k_S}}} = \frac{1}{{{k_1}}} + \frac{1}{{{k_2}}} = \frac{{{k_2} + {k_1}}}{{{k_1}{k_2}}}$
$\frac{1}{{{k_S}}} = \frac{1}{{{k_1}}} + \frac{1}{{{k_2}}} = \frac{{{k_2} + {k_1}}}{{{k_1}{k_2}}}$
$ \Rightarrow {k_S} = \frac{{{k_1}{k_2}}}{{{k_1} + {k_2}}}$.
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