# Why is resultant displacement in an composition of simple harmonic motion the sum of individual displacements?

I recently came across the concept of the composition in simple harmonic motion. A paragraph says that: If

$$x_1 = A_1sin(\omega t)$$

$$x_2 = A_1sin(\omega t + \phi)$$

Then, the resultant displacement is $$x_1 + x_2$$

But what is exactly happening in this case that we are adding these positions? Are we assuming that the particle is initially and origin and forces f1 and f2 act on the body which cause the SHMs?