what is the relationship between R and R1 and R3 for R.cos(wt+β​)=R1.cos(w​t+β)+R3.co​s(3wt+3β)

With R =squrt(R1^2+R3^2) for R.cos(wt+β)=R1.cos(wt+β)+R3.cos(wt+β)

[Torsten]

I don't understand your question.

[Sam Chak]

@YOUSSEF El MOUSSATI, Has this question been resolved? If not, could you please provide constructive feedback and comments to guide further follow-up and discussion?

Answer 1

[Walter Roberson]

syms R R1 R3 w t beta
eqn1 = R == sqrt(R1^2 + R3^2);
eqn2 = R .* cos(w * t + beta) == R1 .* cos(w*t + beta) + R3 .* cos(w*t + beta);

sol = solve([eqn1, eqn2], [R1, R3])

Warning: Possibly spurious solutions.

sol = struct with fields:
    R1: [2×1 sym]
    R3: [2×1 sym]

sol.R1

ans = 

sol.R3

ans = 

So the relationship is that R1 = R and R3 = 0, OR R1 = 0 and R3 = R