The problem of a spring that pulls a weight

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If you read some material from physics, you will read about the experiment with the spring and the weight. The spring gives a force that is F=KX where F is the force that the spring uses on the weight, K is the spring constant (how many Newtons per meter of stretch the spring gives) and X is the distance from the zero point , the distance we stretch the spring. The cycle time of that kind of motion is calculated with a differential equation theory. I won't get into that. If you want, you can challenge yourself and program the process: You need some parameters like K,F,X,M ( the weight mass) and the time parameter. (you will also need more parameters like velocity of the weight and some additions to some of the parameters). If you look at the process of the motion, during the small time fragment, the acceleration of the weight is pretty much the same, so the weight gets some addition to the velocity. That addition is the acceleration multiplied by the time. The weight also made some distance addition toward the zero point. dx=vt+att/2. After some time pieces, if the time pieces are small enough, you will get the result where the force of the spring is zero , the weight made it to the zero point. If you sum all the time pieces, you will get 1/4 of the cycle time. If you want to make that experiment, I suggest you to make a procedure where you set the first parameters , give them values like in the real experiments. then, use the formulas of newton laws and assume the acceleration each iteration is constant during that iteration. What do you think about that kind of program ? With programs like those, one can illustrate pretty much how things are in reality. I got a result that was pretty much accurate when I put some real values to the parameters.