The flux-line-lattice response to AC magnetic fields in type-II superconductors is determined by the shape of the flux pinning potential in the material. This response is normally well described within the Bean critical state model, provided the amplitude of the AC magnetic field is sufficient to unpin and move the vortices from their pinning sites, leading to hysteresis. Conversely, if the vortices remain within their potential wells, their movement remains reversible, and cannot be described by the Bean critical state model. Instead, the mixed state can be viewed as an ensemble of coupled linear harmonic oscillators, each oscillating within its potential well. This is explained by the Campbell model, which extends upon the Bean model to include the finite size of the pinning potential, and a corresponding linear and elastic pinning force. Here, the dynamic equations for flux movement – given a linear pinning force – are described, linearized, and solved analytically. Subsequently, the solution is used to extract the value of the Campbell penetration depth of an applied AC magnetic field from experimental data obtained with a pick-up method.