Porous or biological materials comprise a multitude of micro-domainscontaining water. Diffusion-weighted magnetic resonance measurements are sensitive to the anisotropy of the thermal motion of such water. This anisotropy can bedue to the domain shape, as well as the (lack of) dispersion in their orientations.Averaging over measurements that span all orientations is a trick to suppress thelatter, thereby untangling it from the influence of the domains’ anisotropy on thesignal. Here, we consider domains whose anisotropy is modeled as being the resultof a Hookean (spring) force, which has the advantage of having a Gaussian diffusionpropagator while still confining the spatial range for the diffusing particles. In fact,this confinement model is the effective model of restricted diffusion when diffusion isencoded via gradients of long durations, making the model relevant to a broad rangeof studies aiming to characterize porous media with microscopic subdomains. In thisstudy, analytical expressions for the powder-averaged signal under this assumptionare given for so-called single and double diffusion encoding schemes, which sensitize the MR signal to the diffusive displacement of particles in, respectively, one ortwo consecutive time intervals. The signal for one-dimensional diffusion is shownto exhibit power-law dependence on the gradient strength while its coefficient bearssignatures of restricted diffusion.