We present NMR spectra of liquid 3He, confined to a cylindrical cell, in the temperature range from 2.3 to 1000 mK for a static field of 11.33 tesla and range of applied field gradients. The spectra are generated by taking the Fourier transform of the free induction decay (FID) following NMR tipping pulses. For small tipping angles, the spectra exhibit sharp lines which correspond to long-lived modes with decay times greater than 100 ms. The cause of these magneto-dynamic modes is oscillation of the transverse magnetisation in the applied magnetic field and the demagnetising field. The frequencies of the modes for a given field gradient are independent of temperature, but their damping depends on the effective spin diffusion coefficient which is determined by the Leggett-Rice effect. We also investigate how the spectrum changes with the magnetisation. We are able to simulate the spectra using a model that includes the demagnetising field. The predicted spectral-line frequencies are in reasonable agreement with experiment when there is an applied field gradient. The damping of the modes is due to diffusion, but because of the finite size of the matrices used in the calculation, we have found it necessary to increase the effective diffusion coefficient in the model above the experimental value in order to obtain a spectrum which resembles the experimental one.
