The effective spring constant of two spring system as shown in figure will be
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(a)When external force is applied, one spring gets extended and another one gets contracted by the same distance hence force due to two springs act in same direction.
i.e. $F = {F_1} + {F_2}$
==> $ - \,kx = - \,{k_1}x - {k_2}x$
$\Rightarrow $$k = {k_1} + {k_2}$
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