In this case the frequency of the oscillator is determined by the values of the capacitor and inductor: C and L. Notice that I have now added a diode and another capacitor 10C (10 times bigger than C). The oscillations across the ends of L are a sinewave, varying above and below the Gnd (battery -ve) terminal.
I have connected a diode to the end of L, and coupled this to a potentiometer. The pot provides a variable voltage, from 0 to +3v in my example. As soon as the oscillations exceed the potetiometer voltage, then capacitor 10C is switched in circuit, extending the period time of the oscillations. I chose 3v because in the last oscillator I measured the level was +/-3v from peak-to-peak.
The overall effect is to lower the oscillator frequency by changing VR1. Maximum voltage should be equal to no frequency shift. This technique can give a VERY wide frequency shift, although distortion is present due to an asymetric waveform. The circuit does therefore need some form of post filtering, but since there should also be a buffer then the addition of a low-pass filter should be easily implemented.