A huge problem comes when you start the circuit without a steel tool in the coil. Then he coils are air core and about 1% he inductance of when an iron bar is filling most of the space. This higher inductance lowers the oscillation frequncy oscillation and energy transfer to the workpiece is greatly reduced at 10kHz - (usually inductive heating is at 30KHz to 150kHz).
What else happens at lower fequency? The inductive reactance is much lower at low frequency. But your wave shape will change if your cap bank drains too quickly (before a complete half-cycle. At that point, you have pure DC current flowing (100+ amps) based only on the dc resistance of the coil's copper wire and nearly zero inductive reactance.
Use an H-bridge as
tcmtech suggests to eliminate the presence/absence/cross-section diameter/alloy of a work piece from controlling oscillator frequency, energy transmission to the workpiece and heating.