Need info about oscillator and sensor

I build a 5 [MHz] oscillator
This is for a belt coil sensor that change the induction
This electronic circuit also has a battery
The output is sinus voltage
I need to calculate the right value of the oscilator component
I search after the name of this sensor and this oscillators

It's Colpitts oscillator.

The instrument used for measuring chest expansion/compression is called plethysmograph.