I have a schematic of low pass sallen key which does not include the supply rails and it is to be taken as an ideal op amp with no supply limits and no compensation cap etc.. My derivation from first principles is ready and correct.

I need to find out the range of values of gain for which the output is not sinusoidal when a unit impulse is applied at the input. My equations are:

s-domain (attached)

 

I also need to understand why in Filter responses: (Butterworth, Chebyshef and Bessel), they relate pulse inputs with bode plots.