Low pass filter giving sine wave ( triangular wave as input )
Harmonic Block example only causes ringing

Since the fundamental sine wave is actually 27% higher than the square wave, it is easy to induce ringing from impedance mismatch and block filters that simply truncate harmonics.  

One example is by eliminating all above 5f  of a squarewave, namely only 1f, 3f and 5f, you can see that the fundamental 1f is greater than the squarewave peak by 27% and ringing appears.  That would be a "brick LP filter" just above 5f with 1f = 222 Hz and LPF =1kHz.



High Q filters can cause ringing

A low pass filter with under-damped qualities or Q> 0.707 is what you have. 
However it is possible to eliminate the ringing by low Q filters &lt;0.7.   It is possible to choose a Bessel or Elliptical Filter and Cauer Filters to suppress this harmonic ringing. High order maximally flat Group Delay filters or linear phase shift also have this property of reducing overshoot. These are chosen due to their flat group delay or more linear phase shift properties. ( I will avoid the details here)

Here are 2 examples of 1kHz LPF's . See that the Chebychev filter is more like a brick wall filter such as used to show a 250 Hz square wave with only 1f 3f 5f and cutoff at 1kHz will have ringing or overshoot.

 



Any questions?


  " if the same logic can be used to understand the output of the filter"
  same logic ? 


It is a  principal of harmonic attenuation  or ratio in -dB per octave and also phase shift as some other measurement.

Your sine has triangles that are ~ approx 19x f of the sine wave or 2,4,8,16 approximately 4 octaves at -6dB/octave per order filter so one can expect >-24dB per order filter of suppression of the big triangles.