## Abstract

The vertical motion of a neutrally buoyant float is determined from the solution to the nonlinear forced harmonic oscillator equation originally set forth by Voorhis. Float response to forced vertical oscillations is characterized by the response ratio, *r* = ξ_{r}/ξ_{w}, where ξ_{r}, is the vertical displacement of an isopycnal relative to the float, and ξ_{w} is the vertical displacement of an isopycnal relative to its initial equilibrium position. For isopycnal displacements with frequencies much less than the resonant frequency of the float, the goat can be considered to be in near dynamic equilibrium with the forcing, and *r* is a function of the relative compressibility between the float and seawater, *s* = γ_{f}/ γ_{w}, and the normalized buoyancy frequency *N* = *N*/Ω, where Ω is a characteristic float frequency defined by Ω^{2} = *g*ξ_{w}[1 − (α_{f}α_{w}^{−1})]^{− 1}, where α_{f}, α_{w} are the coefficients of thermal expansion of the float and water, respectively. For the new dynamic equilibrium case, data obtained from a float deployment in a Gulf Stream meander result in an observed *r* value close to the predicted value. For the case of float response to an isopycnal displacement of frequency near the resonant frequency of the float, vertical motion depends on drag, in addition to the material properties of the float and seawater. The bandwidth over which resonance can occur is parametrized by the ‘*Q*’ factor, the inverse of the normalized bandwidth, which for cylindrical floats is predicted to be greater than 1, indicating sharp resonance. From a float deployment in the Gulf Stream region it was estimated that *Q* ≈ 5. For this case, the spectrum of float temperature, which was used as an indicator of the relative response between the float and a displaced isopycnal, and the spectrum of the float pressure, used as an indicator of float displacement, did scale according to that predicted by the condition of near equilibrium response, up to of order the resonant frequency of the float.