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Thank you, So i assume my 1st step is to take the initial condition, model it as SHM, with the solution as the Kernal. *Is the Fourier transform a good pathway to achieving the SHM Core? or, am I better off taking the data inputs and getting SHM equations through the unit circle?

or does eulers formula come in to it after i solve the wave Equation?

Hi, I am trying to model a Particle in Non-Harmonic Motion (Like a spring with Mass oscillator, but with random forces impacting its motion) The data i can take from this is (at a given time) is, - Distance traveled - Displacement (relative to Equilibrium) in the form of '% change' I am trying to model this the SHM formulas x(t), x'(t), x''(t) Do i need to 1st translate the data to the unit circle, with Euler's formula, to then get the PE curve for the object, and solve the SHM formulas from there? I appreciate any clarification on this Thanks in Advance,