We report the design and validation of simple magnetic tweezers for oscillating ferromagnetic beads in the piconewton and nanometer scales. The system is based on a single pair of coaxial coils operating in two sequential modes: permanent magnetization of the beads through a large and brief pulse of magnetic field and generation of magnetic gradients to produce uniaxial oscillatory forces. By using this two step method, the magnetic moment of the beads remains constant during measurements. Therefore, the applied force can be computed and varies linearly with the driving signal. No feedback control is required to produce well defined force oscillations over a wide bandwidth. The design of the coils was optimized to obtain high magnetic fields (280 mT) and gradients (2 T/m) with high homogeneity (5% variation) within the sample. The magnetic tweezers were implemented in an inverted optical microscope with a videomicroscopy-based multiparticle tracking system. The apparatus was validated with 4.5 ¿m magnetite beads obtaining forces up to ~2 pN and subnanometer resolution. The applicability of the device includes microrheology of biopolymer and cell cytoplasm, molecular mechanics, and mechanotransduction in living cells.