A method for estimating drilling parameters of a drill rig for drilling a borehole in an earth material, the method comprising: drilling the borehole with the drill rig in operable communication with a drill string having a mud motor and a drill bit, the drill rig being receptive to adjustable rotational speed of the drill string and adjustable rotational speed of the mud motor; constructing a mathematical model of a system comprising the drill string, the mud motor, and a geometry of the borehole using a processor, the model comprising dimensions, mass distribution, material density, and material stiffness; calculating a mud motor lateral excitation force imposed on the drill string by the mud motor for one or more combinations of drill string rotational speed and mud motor rotational speed using the processor; calculating, with the processor, lateral motion of the drill string and a force imposed on the drill string at a plurality of positions along the drill string for the one or more of combinations of drill string rotational speed and mud motor rotational speed using the mathematical model and the mud motor lateral excitation force; selecting a range of combinations of drill string rotational speed and mud motor rotational speed that result in the force imposed upon the drill string being less than a threshold value using the processor, wherein the drilling parameters comprise the drill string rotational speed and the mud motor rotational speed; and displaying the range of combinations to a user using a display, wherein the displaying comprises displaying a cross-plot of mud motor rotational speed versus drill string rotational speed with a resulting excitation frequency for each combination of mud motor rotational speed and drill string rotational speed, wherein the cross-plot presents areas which are desirable to operate the drill string at those combinations of mud motor rotational speed and drill string rotational speed where the resulting excitation frequencies do not cause the force imposed upon the drill string to exceed the threshold value. drilling the borehole with the drill rig in operable communication with a drill string having a mud motor and a drill bit, the drill rig being receptive to adjustable rotational speed of the drill string and adjustable rotational speed of the mud motor; constructing a mathematical model of a system comprising the drill string, the mud motor, and a geometry of the borehole using a processor, the model comprising dimensions, mass distribution, material density, and material stiffness; calculating a mud motor lateral excitation force imposed on the drill string by the mud motor for one or more combinations of drill string rotational speed and mud motor rotational speed using the processor; calculating, with the processor, lateral motion of the drill string and a force imposed on the drill string at a plurality of positions along the drill string for the one or more of combinations of drill string rotational speed and mud motor rotational speed using the mathematical model and the mud motor lateral excitation force; selecting a range of combinations of drill string rotational speed and mud motor rotational speed that result in the force imposed upon the drill string being less than a threshold value using the processor, wherein the drilling parameters comprise the drill string rotational speed and the mud motor rotational speed; and displaying the range of combinations to a user using a display, wherein the displaying comprises displaying a cross-plot of mud motor rotational speed versus drill string rotational speed with a resulting excitation frequency for each combination of mud motor rotational speed and drill string rotational speed, wherein the cross-plot presents areas which are desirable to operate the drill string at those combinations of mud motor rotational speed and drill string rotational speed where the resulting excitation frequencies do not cause the force imposed upon the drill string to exceed the threshold value.