The unique mechanical and electrical properties of graphene make it an exciting material for nanoelectromechanical systems (NEMS). NEMS resonators with graphene springs facilitate studies of graphene's fundamental material characteristics and thus enable innovative device concepts for applications such as sensors. Here, we demonstrate resonant transducers with ribbon-springs made of double-layer graphene and proof masses made of silicon and study their nonlinear mechanics at resonance both in air and in vacuum by laser Doppler vibrometry. Surprisingly, we observe spring-stiffening and spring-softening at resonance, depending on the graphene spring designs. The measured quality factors of the resonators in a vacuum are between 150 and 350. These results pave the way for a class of ultraminiaturized nanomechanical sensors such as accelerometers by contributing to the understanding of the dynamics of transducers based on graphene ribbons with an attached proof mass.