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Higgs mechanism, through the Higgs field, is responsible for giving mass to elementary particles, including quarks. It's not about oscillation in the sense of a particle's motion, but rather the interaction between quarks and the Higgs field that determines their mass. Quarks, like other fermions, interact with the Higgs field via Yukawa couplings, and the strength of this interaction dictates the mass of the quark. 

Here's a more detailed explanation:

Higgs Field and Mass:The Higgs field permeates all of space and interacts with particles. The strength of this interaction determines a particle's mass. Particles that interact strongly with the Higgs field gain more mass, while those that don't interact at all (like photons) remain massless. 

Quark Interaction:Quarks, being fundamental building blocks of matter, also interact with the Higgs field. The specific way they interact is through what are called Yukawa couplings. 

Yukawa Couplings:These couplings define the strength of the interaction between a quark and the Higgs field. Stronger couplings mean the quark interacts more strongly with the Higgs field and thus has a larger mass. 

No Oscillation in the Usual Sense:While the Higgs field does have quantum fluctuations (Higgs bosons), the "oscillation" related to the Higgs mechanism isn't about the quarks themselves moving back and forth. Instead, it's about how the quarks couple to the field, which determines how much "resistance" they feel from the field and, consequently, their mass. 

Different Masses for Different Quarks:Different quarks have different masses because they have different strengths of interaction with the Higgs field. For example, the top quark, which has the strongest interaction with the Higgs field, has the largest mass.