  Cryogen-free low-temperature setups are becoming more prominent in
experimental science due to their convenience and reliability, and concern
about the increasing scarcity of helium as a natural resource. Despite not
having any moving parts at the cold end, pulse tube cryocoolers introduce
vibrations that can be detrimental to the experiments. We characterize the
coupling of these vibrations to the electrical signal observed on cables
installed in a cryogen-free dilution refrigerator. The dominant electrical
noise is in the 5 to 10 kHz range and its magnitude is found to be strongly
temperature dependent. We test the performance of different cables designed to
diagnose and tackle the noise, and find triboelectrics to be the dominant
mechanism coupling the vibrations to the electrical signal. Flattening a
semi-rigid cable or jacketing a flexible cable in order to restrict movement
within the cable, successfully reduces the noise level by over an order of
magnitude. Furthermore, we characterize the effect of the pulse tube vibrations
on an electron spin qubit device in this setup. Coherence measurements are used
to map out the spectrum of the noise experienced by the qubit, revealing
spectral components matching the spectral signature of the pulse tube.
