Solve the following equation using Wolfram Language?

Questions
,
1

Hi everyone,

I should solve an equation which is as follows:

a*(1-cos(w*x))+bx=z

(a,b,w,z) are parameters.

I want the answer of x, but I cant find it anywhere,

It would be a great help if you can solve it,

Sincerely,

2

This is a way:

Manipulate[
 Quiet@Reduce[
   a (1 - Cos[w x]) + b*x == z &&
    Abs[z - b*x] <= 2 Abs[a],
   x, Reals],
 {a, -5, 5}, {b, -5, 5}, {w, -5, 5}, {z, -5, 5}]
3

Thank you so much for your help,

I want to solve and find a formula for x,

in reality, this is a periodical equation and (x) is the time that the waveform goes to zero,

5<a<15 , -20e+6<b<-2e+6 , 10<z<13 , 1e+6<w<10e+6

I wanted to use your way but I couldn’t find the last formula for (x) ,

is it possible for you to help me more?

Thank you so much for the time that you give me,

Sincerely,

Ramtin

4

The equation is trascendental. I don’t think you can find an explicit formula, and often there is more than one solution.