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Getting from Particle in Non-harmonic Motion, to SHM Formulas


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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,

Edited by blablablabla
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5 hours ago, blablablabla said:

but with random forces impacting its motion)

Here is your biggest hurdle.


This makes the system non conservative.

SHM represents a conservative system.


That said when we consider the eqautions of SHM we equate the sums of system forces or energies to zero (because it is conservative)

We can introduce non conserative 'forcing functions' by equating an SHM system to the forcing function.

Normally we then try to solve the result by building onto the solutions to the SHM core (or 'kernal').

Edited by studiot
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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?

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