Analysis for Loop #1 using the dispersionless model. Top left: loop position (symbols) as a function of time is described by our model (green line) which includes a background trend (blue line) described by our spline procedure. The red shaded region represents the 99% credible intervals for the loop position predicted by the model, including an estimated noise σ_Y. The dotted and dashed lines denote t₀ and t_s1, respectively. Top right: wavelet analysis of the loop position with colours representing the normalised spectral amplitude. The dashed lines show the time-dependent periods of oscillation described by our model. The hatched region denotes the cone of influence. Middle left: detrended loop position (symbols) with the first (green), second (blue), and third (red) longitudinal harmonics. Times t_s1, t_s2, and t_s3 are denoted by the dashed lines in the corresponding colour. Middle right: density profile parameters determined by the oscillation damping envelope. The red bars are based on the median values and the 95% credible intervals, indicated by the dotted and dashed lines, respectively, in the histograms (bottom panels). The solid curves are fits to the histogram data using the exponentially modified Gaussian function.