Phi-bits, the classical mechanical analogs of qubits, play a pivotal role in the development of quantum-analog computing systems. Understanding the nonlinear processes governing control and interconnectivity among phi-bits is imperative for their advancement. These phi-bits, existing as acoustic waves within arrays of interconnected waveguides, exhibit a remarkable ability to maintain coherent superpositions of two states under external nonlinear driving forces. Manipulating the frequency, amplitude, and phase of external drivers allows precise control over phi-bit states. To analyze and predict the nonlinear response of phi-bits to external stimuli, we have developed a discrete element model. This model comprehensively captures various types, strengths, and orders of nonlinearities stemming from intrinsic medium coupling between waveguides and external factors like signal generators, transducers, and ultrasonic couplant assemblies. Our study unveils significant insight, highlighting how nonlinearity type, strength, order, and damping impact the complex amplitudes' modulus and phases in the coherent superposition of phi-bit states, with a notable impact on their predictability and stability, particularly at high damping levels. This investigation explores the controlled creation of phi-bits to observe the superposition of states, essential for advancing phi-bit-based quantum analogue information processing platforms.