We propose a simple and inexpensive method to directly observe each normal mode of a system of coupled oscillators, as well as to measure its corresponding frequency, without performing Fourier analysis or using expensive apparatus. The method consists of applying a frequency dependent force to the system and using the resonance to excite each mode separately. The frequency of the excited mode is determined by measuring the resonance frequency of the system. We found that the measured normal mode frequencies of coupled oscillators exhibiting two and three normal modes are in very good agreement with the theoretical estimates. The method is suitable for undergraduate students with an elementary knowledge of differential equations.

We discuss a time-of-flight measurement of the speed of light which is inexpensive to build, has an experimental design completely accessible to students with a rudimentary knowledge of interference, and consistently produces values for c with errors of less than 1%. Students at the sophomore level can use the same apparatus to achieve uncertainties on the order of 0.25%.