# Why do particles in particle swarm optimization converge to the global best when their personal best has just as much weight?

I know this is probably a really basic question but I just cant wrap my head around it right now.
So the basic PSO update formula is as follows: $$\bar{v}_{n+1} = \omega \cdot \bar{v}_n + c_k \cdot r_1 \cdot (\bar{p}_{best}-\bar{p}_n)+ c_s\cdot r_2 \cdot (\bar{g}_{best}-\bar{p}_n)$$ velocity(n+1) = momentum_component + cognitive_component + social_component

Now both the cognitive part and the social part have the same weight to them on the updated velocity.
So when a particle is moving around the space and lets say the cognitive part pulls the particle in a certain direction while the social component pulls the particle in the opposite direction, shouldnt the particle be stuck forever? Or at least go back and forth never converging?

However if I run the basic vanilla PSO algorithm the particles always seem to converge to the gbest as if their pbest has barely any influence.