# How can amplitudes be treated as vectors in Simple Harmonic motion?

The amplitudes of 2 SHM are scalors. When we combine the two SHM eq.(lying along the same line), the resultant expression becomes of amplitudes treated as vectors and the phase angle between them as the angle b/w the vectors. How can we add them vectorically if they are not vectors but scalors?

For mathematical convenience, $\sin(\omega t + \phi_0)$ can be viewed as the imaginary part of $e^{i(\omega t + \phi_0)}$ (exponential functions are much easier to work with than goniometric functions. This is the same as seeing the link between a SHM and a constant rotational movement: the SHM is the projection of the rotation, a can be viewed in the picture below:
The projection of the rotating vector $\vec{A}$ with rotational velocity $\omega$, is a SHM with amplitude A (scalar)