On the smallest oscillations of rigid and flexible bodies. A new and easy method.
This is Euler's first paper on vibrating bars. He integrates the differential equation k4y''' = y using power series. (Based on Clifford Truesdell's An idiot's fugitive essays on science: methods, criticisms, training, circumstances.)
Original Source Citation
Commentarii academiae scientiarum Petropolitanae, Volume 7, pp. 99-122.
Opera Omnia Citation
Series 2, Volume 10, pp.17-34.