When we go for a walk with friends, we can observe an interesting effect: From step lengths to arm movements - our movements unconsciously align; they synchronize. Prior research found that this synchronization is a crucial aspect of human relations that strengthens social cohesion and trust. Generalizing from these findings in synchronization theory, we propose a dynamical approach that can be applied in the design of non-humanoid robots to increase trust. We contribute the results of a controlled experiment with 51 participants exploring our concept in a between-subjects design. For this, we built a prototype of a simple non-humanoid robot that can bend to follow human movements and vary the movement synchronization patterns. We found that synchronized movements lead to significantly higher ratings in an established questionnaire on trust between people and automation but did not influence the willingness to spend money in a trust game.