We present the theory used to analyse experiments at Manchester University in which we observe the normal modes of transverse vibration of a Kapton diaphragm separating two nominally identical disc-shaped regions of superfluid 3He, each of height 100 μm and diameter 40 mm. From the mode frequencies we deduce information on the superfluid density and hence on strong coupling corrections to the energy gap. From the dissipation the first and second viscosities, η and ξ3, of the fluid can be obtained. Rotation of the experiment about an axis perpendicular to the diaphragm creates a lattice of quantised vortex lines. We show how the mutual friction parameters B and B′ can be determined from the effect of the vortices on the normal modes of the diaphragm.