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Background:

My software has a timeline where I can input the time. I also have the X-axis where I can output the location.

Goal:

I want to simulate the inertia motion of two objects (one main object affects the other).

My research:

This equation gives damping oscillations of the affected object.

x=e^(-t)*sin(t)

I can input or vary the time (t) using my timeline. The output (x) works well. Click here to visualize the equation.

Question:

This equation is not related to the inertia or the acceleration of the main object. I can measure the acceleration (a) of the main object. How can I add it to the equation so that the inputs are (t) and (a) and the output is (x)?

If there is acceleration, the affected object should start with the initial velocity of the main object then end with the effect of the damping equation.

user2824371
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    You can take the second derivative of $x$ to get the acceleration. You can then formulate a differential equation that $x$ satisfies. I don't know if that is what you want. – Ross Millikan Jul 16 '21 at 17:59
  • @RossMillikan Sounds a good I dea! Thank you so much, I'll try it and get back to you later. – user2824371 Jul 17 '21 at 20:30

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