Why signal coming out of a Constant K filter takes 0.5ms to stabilize?
Why signal coming out of a Constant K filter takes 0.5ms to stabilize?


and


  why does that happen


It's called the transient response - you can't expect a filter to immediately start producing the steady AC response from an initial application of a sinewave. At the point of initially applying a sinewave, the input signal goes from a steady value of zero to a half sine pulse. The filter does not know in those first few moments that what is being applied to it is a sinewave. It cannot predict the future hence, it does what it does and eventually settle to the steady-state AC response (as all filters do).


  how can it be corrected?


It can't. It is what it is.