# Superposed simple harmonic oscillators

When deriving the equation for the superposed amplitude:

$$A^2=A_1^2+A_2^2+2A_1A_2 \cos(\phi_2-\phi_1)$$

From $$x_1(t)=A_1 \cos(\omega t+\phi_1)$$and $$x_2(t)=A_2 \cos(\omega t+\phi_2)$$

How do you determine which way the phase differences should be within the cos? Some examples I have seen say it is $$\phi_1-\phi_2$$ but it was shown as $$\phi_2-\phi_1$$ in my lecture notes.

• I think we use a modulus instead of brackets. This will probably solve your confusion! – Creepy Creature Oct 15 '19 at 19:09