The oscillations of a small magnetic sphere (radius 100 μm) levitated above a superconductor are investigated. Resonance frequencies between 300 Hz and 600 Hz are observed. At low amplitudes (≤1 gmm) the oscillator has Q values of about 106. At larger amplitudes both the resonance frequency and the damping become amplitude dependent. Nonlinear and hysteretic friction is attributed to vortex motion in the superconducting environment. Application of this oscillator for investigation of vorticity in superfluids is discussed.