Long-range interactions between cold Rydberg atoms are being investigated for neutral-atom quantum computing, quantum simulations, phase transitions in cold Rydberg gases and other applications. Fine tuning of the interaction strength can be implemented using Förster resonances between Rydberg atoms controlled by an electric field. The observation of the Stark-tuned Förster resonances between Rydberg atoms excited by narrowband cw laser radiation requires usage of a Stark-switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field, which is scanned across the Förster resonance. The application of the radio-frequency field causes additional Förster resonances between collective states, whose line shape depends on the interaction strengths and time. Spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the Förster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned Förster resonances Rb(nP 3/2) + Rb(nP 3/2) → Rb(nS 1/2) + Rb([n + 1]S 1/2) for two Rb Rydberg atoms interacting in a time-varying electric field.