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We present micro-magnetic simulations of the effects of switching field rise time on magnetization reversal for both exchange spring media (ESM) and single phase media (SPM). Numerical results yield the following. 1) As the rise time of switching field pulse decreases in a specific range, the coercivities of both medium for ESM and SPM drop significantly. This phenomenon is more obvious when the microwave frequency deviates from optimal frequencies where coercivities drops to a minimum. 2) The optimal frequency of ESM is lower than that of SPM. It becomes even lower as the rise time decreases. 3) With rise time ranging, oscillation of optimal frequency of ESM is lower than that of SPM. It decreases further as the rise time decreases. 4) For different rise times, oscillations of optimal frequencies coercivities occur in the simulations. This phenomenon is more obvious for SPM than that for ESM. We also observe that for larger damping constants in the ESM model, the optimal frequency coercivity fluctuations decrease gradually.