Long burst of high amplitude noise removal
If I understand you correctly, then your issue is connected with transient that is present when switching on your device, because it is a RLC circuit. Most likely these spikes are not changing over time (because values of passive components are constant), if so, then you can:

Create the template of such spike and use the normalised correlation for detection. If it's above a given threshold, then substitute samples with linear/spline or whatever interpolation.
Use the Matched Filtering approach (which is almost the same as above approach, but offers better SNR performance) and remove detected samples accordingly

If your spikes are of random nature, then there is many methods that are allowing to remove any crackles and clicks. You might refer to the literature for such solutions:

Oudre L. - Automatic detection and removal of impulsive noise in audio signals
Knapp M., Bashir R. - Audio Click Removal using LPC
Godsil S., Rayner P. - Digital Audio Restoration
Alvarez E., et al. - Detection of clicks using sinusoidal modelling for the confirmation of the clicks