Explanation:
Here, \(L_{1}=L, C_{1}=C\),
Resonant frequency, \({\omega _0} = \frac{1}{{\sqrt {LC} }}\,\,\,\,\,\,\,\left( 1 \right)\)
Now, \(L_{2}=2 L, C_{2}=8 C\)
So, \(\omega_{2}=\dfrac{1}{\sqrt{2 L \times 8 C}}=\dfrac{1}{4} \times \dfrac{1}{\sqrt{L C}}=\dfrac{\omega_{0}}{4}\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm{(from (1))}}\,\)
So, \(x=1 / 4\)