Resonance is mainly a sine signal because a resonance is at only one frequency, only one frequency is a narrow spectrum and a narrow spectrum implies a sine signal, consequence of the Fourier transform.
If you don't observe a sine shape, you may forget resonance.
The waveshape across the resonant components can
be of high spectral purity if the circuit is only very
lightly loaded.
In the case of industrial applications, the resonant
components are typically very heavily loaded so the
resultant waveshape is heavily damped. A damped
oscillation is by its very nature not a pure sinusoid
as the loading induced distortion produces harmonics
and modulation products.
In high power industrial applications this distortion
is quite tolerable.
In the single ended Induction Cooker waveshape the
driven half cycle of resonance is significantly larger
than the free-wheeling circulating current half cycle
due to energy transfer to the load. Since the oscillation
is reinforced each cycle by the driver circuit the desired
resonance is sustained even though the resultant
waveshape is lop-sided. The conditions of resonance
are met. DC input pulses result in an alternating current
within the resonant components.
Conversion is accomplished.
It may be instructive to monitor the output waveshape
of the Induction Cooker while it is "ON" but not yet loaded
by any metallic surface in proximity to the output coil.
Once "loading" is detected by the Control Circuits then
the Cooker will shift to normal high power output.
Ex's understanding of "resonance" seems to be predominantly
theoretical and he may lack actual experience with the plethora
of resonant circuits in common usage in other than Radio
Frequency Communications devices.
For there is nothing hidden that will not be disclosed, and nothing concealed that will not be known or brought out into the open.