Drag on an axially symmetric body vibrating slowly along its axis in a viscous fluid

Let D0 be the Stokes drag on an axially symmetric body moving parallel to its axis with velocity U0 through an unbounded fluid. The drag D experienced by the same body oscillating with velocity U = U0eiσt along its axis in the unbounded fluid is given by the expression D/D₀ = \1 + d₀6 (2) π μ a U₀(1+i)M+O(M²) σ t, where a is any characteristic particle dimension and M² = a² σ ρ |μ is a dimensionaless number. The part of this drag formula which gives the energy dissipation is calculated for bodies of various shapes.