Potential energy - damping energy = kinetic energy? So if you can sum up the total damping energy (probably wasted energy such as friction or air drag) and the kinetic energy obtained, you should be able to calculate how much potential energy was needed, to get that process started.
Work is energy transferred. Or are you asking something more obscure?
Appreciated for your concern, my point of view is : if we could with somehow measure the kinetic energy and potential energy for some structure and connected transducer, could we calculate the exerted work done by the transducer ?
Mostafa, a transducer does not exert a force or work. Not appreciably, anyway. It measures force. Maybe it would help to know more precisely what you are trying to model.
Work is energy in motion. Hence, chemical potential energy remains faithful to the fundamental law: potential energy is converted to kinetic energy and never created or destroyed.