Oscillators with LC feedback circuits
An LC Oscillator converts a DC input into an AC output. This  output waveform can have a wide range of different shapes and  frequencies, and can be either complex in shape, or be a simple pure  sine wave depending upon the application. An Oscillator is  basically an Amplifier with Positive Feedback, or regenerative feedback  and one of the many problems in electronic circuit design is stopping  amplifiers from oscillating while trying to get oscillators to  oscillate. Oscillators work because they overcome the losses of their  feedback resonator circuit either in the form of a capacitor, inductor or  both in the same circuit by applying DC energy at the required  frequency into this resonator circuit. In other words, an oscillator is a  an amplifier which uses positive feedback that generates an output  frequency without the use of an externally applied input signal.
Piezoelectric materials and their applications
Crystal Oscillators, A  piezoelectric crystal will vibrate naturally in several mechanical  modes, the frequencies of vibration being dependent on the dimensions of  the specimen and the elastic constants of the material (f = 1/2l  √Y/√ρ). If the crystal is placed between electrode and an alternating  voltage at one of the resonant frequencies is applied, the amplitude of  oscillation will build up at this frequency.
Transducer, Acoustic pulses are  used in underwater search and other applications. In almost all such  cases the acoustic pulses are produced by piezoelectric transducers  shock excited by electric fields.
Delay Lines, the  piezoelectric materials can be used as delay lines. If an electrical  signal is converted into an acoustic one at one end of a quartz rod, the  signal will pass along the rod as an acoustic wave. It will travel in  the quartz with the appropriate sound velocity. On reaching the end of  the rod, the acoustic wave may be picked off as an electrical signal.  The initial electrical signal has been delayed; a requirement often found in communication devices.
References: 
LC Oscillator Tutorial and Tuned LC Oscillator Basics (electronics-tutorials.ws) 
 Links to an external site.
Applications of Piezoelectric Materials | Electrical Engineering (engineeringenotes.com)