d
For figure \((a):\)

\(K _{\text {oq }}=\frac{ K \times 2 K }{ K +2 K }=\frac{2 K }{3}\)

\(T =2 \pi \sqrt{\frac{ m }{ K _{ eq }}}=2 \pi \sqrt{\frac{ m }{2 K / 3}}=2 \pi \sqrt{\frac{3 m }{2 K }}\)

For figure \((b):\)

\(K _{ eq }=3 K , T ^{\prime}=2 \pi \sqrt{\frac{ m }{3 K }}\)

\(\frac{ T ^{\prime}}{ T }=\sqrt{\frac{ m \times 2 K }{3 K \times 3 m }}=\frac{\sqrt{2}}{3}\)

\(T ^{\prime}=\sqrt{2}\)

\(x =2\)