Two Superposed Vibrations of Equal Frequency

[EP]

The Problem
A particle is simultaneously subjected to three simple harmonic motions, all of the same frequency and in the x direction. If the amplitudes are 0.25, .20, and 0.15 mm, respectively, and the phase difference between the first and second is 45, and between the second and third is 30, find the amplitude of the resultant displacement and its phase relative to the first (0.25 mm amplitude) component.

I drew a diagram and of the vectors but the equations I have are all for two vectors systems. How do I start this problem off?

 

[zigga15]

Start by assuming the 0.25mm wave is fully dispacing the particle, so its moving it 0.25mm from equilibrium position. the difference between the first and the second is 45 degrees so it will effect it as per the phase its in at that time.