  We use a guiding center code ORBIT to study the broadening of resonances and
the parametric dependence of the resonance frequency broadening width
$\Delta\Omega$ on the nonlinear particle trapping frequency $\omega_b$ of
wave-particle interaction with specific examples using realistic equilibrium
DIII-D shot 159243 (Collins et al. 2016 Phys. Rev. Lett. 116 095001). When the
mode amplitude is small, the pendulum approximation for energetic particle
dynamics near the resonance is found to be applicable and the ratio of the
resonance frequency width to the deeply trapped bounce frequency
$\Delta\Omega/\omega_b$ equals 4, as predicted by theory. This factor 4 is
demonstrated for the first time in realistic instability conditions. It is
found that as the mode amplitude increases, the coefficient
$a=\Delta\Omega/\omega_b$ becomes increasingly smaller because of the breaking
down of the nonlinear pendulum approximation for the wave-particle interaction.
