I think you have seriously misunderstood something. "Particles" do not oscillate in QM or QFT. The formal QM description of matter would state that the elementary constituents of matter can behave as a particle and/or a wave. More technically, the wave function we get from Schrodinger's equation describes a probability distribution for observing a particular state of the "particle". This is how the two concepts are married in QM. QFT goes a bit further in asserting that the classical object being quantized is a field. The quantized field states are described as occupation operators are their states describe the number of "particles" one has in a given classical state, e.g. with some momentum, location, etc. The QFT description is sometimes called second quantization but many modern theorists do not use this terminology anymore.
The field is described by a linear wave equation and those states are always "vibrating", or oscillating. This may be where the confusion comes from. But the particle being described by the QFT solution is not in any way attached to a spring or oscillating because of this.