  Using finite element micromagnetic simulations, we study how resonant
magnetisation dynamics in thin magnetic discs with perpendicular anisotropy are
influenced by magnetostatic coupling to a magnetic nanoparticle. We identify
resonant modes within the disc using direct magnetic eigenmode calculations and
study how their frequencies and profiles are changed by the nanoparticle's
stray magnetic field. We demonstrate that particles can generate shifts in the
resonant frequency of the disc's fundamental mode which exceed resonance
linewidths in recently studied spin torque oscillator devices. Importantly, it
is shown that the simulated shifts can be maintained over large field ranges
(here up to 1T). This is because the resonant dynamics (the basis of
nanoparticle detection here) respond directly to the nanoparticle stray field,
i.e. detection does not rely on nanoparticle-induced changes to the magnetic
ground state of the disk. A consequence of this is that in the case of small
disc-particle separations, sensitivities to the particle are highly mode- and
particle-position-dependent, with frequency shifts being maximised when the
intense stray field localised directly beneath the particle can act on a large
proportion of the disc's spins that are undergoing high amplitude precession.
