I have 2 simple harmonic motions and I want to compose them on the same axis. So:
x1 = A1*sin(ω1*t+θ1)
x2 = A2*sin(ω2*t+θ2)
The goal is to find the resultant motion of these 2 in the form:
X = A*sin(ω*t+Θ), so to find A,ω and Θ as functions of A1,A2,ω1,ω2,θ1 and θ2.
2. Relevant equations
I believe there is an analytical way and a graphical way(Fresnel graph) to solve this .