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I made a force diagram into a matrix. How can I have find a value in y for a number in x? I know for 0.1 for example the force becomes 500, or for 0.3 it becomes -500 How do I know how much it will be for .1234

p = ( {
    {0, 0},
    {.2, 1000},
    {.4, 0},
    {.6, -1000},
    {.8, 0}
   } );
ListLinePlot[p]

enter image description here

Improve this question
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  • $\begingroup$ i use this but it give me wrong answers Interpolation[p, .1] $\endgroup$
    – Scott Constantine
    Dec 1, 2020 at 17:48

1 Answer 1

Reset to default
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Clear["Global`*"]

p = {{0, 0}, {.2, 1000}, {.4, 0}, {.6, -1000}, {.8, 0}};

Use Interpolation

f = Interpolation[p];

f[0.1234]

(* 962.25 *)

Plot[f[x], {x, 0, 0.8},
 Epilog -> {AbsolutePointSize[6],
   Red, Point[p], Green, Point[{#, f[#]} &[0.1234]]}]

enter image description here

Edit: If you want linear interpolation change the InterpolationOrder to 1

f2 = Interpolation[p, InterpolationOrder -> 1];

f2[0.1234]

(* 617. *)

Plot[f2[x], {x, 0, 0.8}, 
 Epilog -> {AbsolutePointSize[6], Red, Point[p], Green, 
   Point[{#, f2[#]} &[0.1234]]}]

enter image description here

Improve this answer
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  • $\begingroup$ that's my problem, my digram is liner not like something you say, in fact I have diagram and I want Interpolation it $\endgroup$
    – Scott Constantine
    Dec 1, 2020 at 18:04
  • $\begingroup$ tanks a lot, i have jus on more questions ,My steps for t are 0.1 from zero to two. How can I write this formula? c = Subscript[t, i] + Subscript[t, i + 1] c=t(i)+t(i+1) $\endgroup$
    – Scott Constantine
    Dec 1, 2020 at 18:46
  • $\begingroup$ Your comment doesn't make any sense to me. You have not explained how c or t relates to anything previously discussed. If t is the domain of f, the interval {0.1, 2} extends well beyond the basis for the interpolation (i.e., {0, 0.8}) and would require extrapolation rather than interpolation. If so, what is the expected behavior outside of the origin range? Linear? Periodic? You want to know "how to write a formula" but you have not said what the formula is to represent other than the formula that you gave. Please formulate your question better and post as a new question. $\endgroup$
    – Bob Hanlon
    Dec 1, 2020 at 20:55
  • $\begingroup$ Hi, I said my question has nothing to do with the previous one,Suppose I have this formula t={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} How to calculate c=t(i)+t(i+1) $\endgroup$
    – Scott Constantine
    Dec 1, 2020 at 22:13
  • $\begingroup$ New questions should not be asked in comments. $\endgroup$
    – Bob Hanlon
    Dec 1, 2020 at 22:17

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