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The classical vibrational metastable states in a one-dimensional two-mass system are investigated experimentally and theoretically via the transmission of a coherent wave packet propagating through the system. The Fourier transform of the vibrational signal recorded in between the masses reveals resonant excitations by the coherent wave packet. The time-resolved spectrum indicates that the lifetime of a metastable state of higher frequency is longer than that of lower frequency, which is in contrast with the quantum mechanical double-barrier system. This study, which is easily accessible to physics majors, also demonstrates quantum resonant tunneling in a very simple classical way.

In this paper we discuss our study of a string–mass chain and its anology to quantum mechanical systems. Theoretical predictions are made based upon the numerical solution to the wave equation. These predictions are tested experimentally using both normal mode analysis and pulse analysis. The frequency band structures for periodic and disordered string mass chains are studied as well as their corresponding eigenfunctions. The theoretical and experimental results are in accord. This experiment, suitable for advanced physics majors, demonstrates many important features of quantum mechanics: eigenvalues, superposition principle, band structure, gap modes, and Anderson localization.