  A theoretical expression is derived for the mechanical contribution to the
mean swimming speed of a vibrating two-sphere immersed in a viscous
incompressible fluid. The two spheres are connected by an elastic spring which
provides a harmonic potential for oscillations about a mean distance between
centers. The system is made to oscillate at a chosen frequency by activating
forces which sum to zero. The mechanical contribution to the resulting mean
swimming velocity is calculated from the mechanical equations of motion and the
corresponding impedance matrix of linear response. The frequency-dependent pair
friction coefficients are found from approximate expressions derived earlier.
The mechanical contribution is calculated to second order in the amplitude of
stroke as a function of the scaling number, a dimensionless combination of
size, frequency, and kinematic viscosity. Retarded friction and added mass
determine the functional behavior.
