\begin{table}%t3
\caption{\label{tbl:nonlinear_predictions}Selection of predicted versus observed frequencies under
the assumption of time-dependent amplitudes and phases  (model given by Eq.~(\ref{eq:dominant_mode_time_variable})).}
%\centering
\small
\begin{tabular}{rrrl}
\hline\hline
Component & Secondary & Spurious frequency & Error\\
\hline
$f_1$ & 0.8379 & 6.3248 & Observed \\
$f_1$ & --0.8379 & 4.6490 & Observed \\
$2f_1$ & 0.8379 & 11.8168 & Observed \\ 
$2f_1$ & --0.8379 & 10.1359 & --\\ 
$3f_1$ & 0.8379 & 17.2986 & Observed \\
$3f_1$ & --0.8379 & 10.1359 & --\\
\hline
\end{tabular}
\begin{tabular}{rrrl}
Component & Secondary & Spurious frequency & Error \\ 
\hline
$f_1$  &  1.7678 &  7.2546 & Observed\\
$f_1$  & --1.7678 &  3.7191 & --\\
$2f_1$ &  1.7678 & 12.7412 & Observed\\
$2f_1$ & --1.7678 &  9.2060 & --\\
$3f_1$ &  1.7678 & 18.2285 & --\\
$3f_1$ & --1.7678 & 14.6928 & --\\
\hline
\end{tabular}
\begin{tabular}{rrrl}
Component & Secondary & Spurious frequency & Error\\
\hline
$f_1$  &  2.5650 &  8.0519 & --\\
$f_1$  & --2.5650 &  2.9219 & Observed\\
$2f_1$ &  2.5650 & 13.5388 & --\\
$2f_1$ & --2.5650 &  8.4088 & Observed\\
$3f_1$ &  2.5650 & 19.0257 & --\\
$3f_1$ & --2.5650 & 13.8957 & Observed\\
\hline
\end{tabular}
\end{table}