The relaxation time spectrum can be determined from dynamic shear experiments, also called oscillatory shear experiments.
These experiments are performed on a rheometer, which imposes the different constant shear rates on the material sample and measures the resulting stress. The total shear amplitude has to be sufficiently small to stay within the linear region.
The elastic response is in-phase with the imposed deformation function, while the viscous response is in-phase with the imposed rate of deformation function, or 90 degrees out-of-phase with the imposed deformation function. The viscoelastic response, a combination of the elastic and viscous responses, is out-of-phase with the imposed deformation function, somewhere between 0 and 90 degrees.