A number of studies suggest that shock acceleration with particle feedback and very efficient magnetic-field amplification combined with Alfv{e}nic drift are needed to explain the rather soft radio spectrum and the narrow rims observed for Tychos SNR. We show that the broadband spectrum of Tychos SNR can alternatively be well explained when accounting for stochastic acceleration as a secondary process. The re-acceleration of particles in the turbulent region immediately downstream of the shock should be efficient enough to impact particle spectra over several decades in energy. The so-called Alfv{e}nic drift and particle feedback on the shock structure are not required in this scenario. Additionally, we investigate whether synchrotron losses or magnetic-field damping play a more profound role in the formation of the non-thermal filaments. We solve the full particle transport equation in test-particle mode using hydrodynamic simulations of the SNR plasma flow. The background magnetic field is either computed from the induction equation or follows analytic profiles, depending on the model considered. Fast-mode waves in the downstream region provide the diffusion of particles in momentum space. We show that the broadband spectrum of Tycho can be well explained if magnetic-field damping and stochastic re-acceleration of particles are taken into account. Although not as efficient as standard DSA, stochastic acceleration leaves its imprint on the particle spectra, which is especially notable in the emission at radio wavelengths. We find a lower limit for the post-shock magnetic-field strength $sim330,mathrm{mu G}$, implying efficient amplification even for the magnetic-field damping scenario. For the formation of the filaments in the radio range magnetic-field damping is necessary, while the X-ray filaments are shaped by both the synchrotron losses and magnetic-field damping.
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