Match the data given in the left column with the frequency equations given in the right column for a two-degree-of-freedom system governed by the equations of motion:

\[\begin{aligned}& J_{0} \ddot{\theta}_{1}-2 k_{t} \theta_{1}-k_{t} \theta_{2}=0 \\& 2 J_{0} \ddot{\theta}_{2}-k_{t} \theta_{1}+k_{t} \theta_{2}=0\end{aligned}\]

\(J_{0}=1, k_{t}=2\)

a. \(32 \omega^{4}-20 \omega^{2}+1=0\)

b. \(\omega^{4}-5 \omega^{2}+2=0\)

c. \(\omega^{4}-10 \omega^{2}+8=0\)

d. \(8 \omega^{4}-10 \omega^{2}+1=0\)