The present invention provides a system for performing a suitable operation in a wellbore utilizing a resonator (74). The system includes a resonator (74) for generating pulses of mechanical energy, an engaging device (92) for securely engaging an object in the wellbore and a sensor (68a) for detecting the response of the object to pulses generated by the resonator (74). The resonator (74) is placed at a suitable location in the wellbore and the engaging device (92) is attached to the object. The resonator (74) is operated at an effective frequency to induce pulses into the object. The sensor (68a) detects the response of the object to the induced pulses, which information is utilized to adjust the operating frequency. The system in different configurations can be used to fish, free a stuck drill string, aid drilling of wellbores and to perform a cementing operation. A control circuit (78) controls the operation of the system according to programmed instructions.
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