# Composition of 2 simple harmonic motions with different angular veloci

**1. The problem statement, all variables and given/known data**

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 .

Thanks,

Radu

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