= Solution
Measure <displacement> from each arrangement's gravitational <equilibrium>. The <series and parallel spring stiffness> follows by adding <forces> or extensions. In the parallel arrangement the two <spring> <forces> change by $kx$ each, giving equivalent stiffness $2k$. In series the common <force> $F$ extends each <spring> by $F/k$, so total extension is $2F/k$ and the equivalent stiffness is $k/2$. Hence
$$
\boxed{f_{\parallel}=\frac1{2\pi}\sqrt{\frac{2k}{m}},\qquad f_{\rm series}=\frac1{2\pi}\sqrt{\frac{k}{2m}},\qquad\frac{f_{\parallel}}{f_{\rm series}}=2.}
$$
The corresponding <angular frequencies> are $2\pi f$. <gravity> shifts the <equilibrium> extensions but does not alter the small-oscillation stiffness of these ideal linear, massless <springs>.
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