Find the transfer function given responses
Assuming that the order of six the plots is

(i=1)   (i=2)
(i=3)   (i=4)
(i=5)   (i=6)


And that:


From the first plot, the initial phase is 90º leading (a regular sine would start at 0º)
In the fourth plot, phase lags 90º, so phase become 0º
In the firth plot, it lags an additional 90º, so phase become 180º


Then, also considering the amplitudes, we could sketch a bode plot (like Andy aka suggested - took 5 minutes):



From this, it seems that structure is an derivator (DC gain = 0, positive magnitude slope and phase 90º leading) with two poles (same slope but descending, adds 180º of lag):

$$ Y(s) = \frac{as}{(s+b)(s+c)} U(s) $$ 

(It could actually be a double/triple/"n" integrator with four/six/"2n" poles, you can discover that by checking if the ascending or descending slope of the gain plot is 20 or 40 or 20*n db/decade).

You can then discover the coefficients by substituting \$Y(s)\$ and \$U(s)\$ in the preceding equation by the inputs and outputs (outputs will be the magnitude gain plus the phase lag), also substituting \$s=jw\$.

Hopefully then you will arrive at your answer.