I was told in my class that simple harmonic motion (SHM) describes the motion of the projection onto a straight line of the motion of a particle undergoing uniform circular motion (i.e. with constant angular velocity about the circle's center).
As we know, a spring and pendulum executes SHM but their particles are not moving in circular direction. So how come they have angular frequency? $y$ in the equation describes the position on the projection of particle but as they are not moving in circular what is $y$ describing?
We do we say that a circular motion is a periodic motion but not oscillatory. But we are also saying that it's projection is in SHM. If the original particle is not in SHM, meaning it's not satisfying the condition of SHM, how can it's projection meet those conditions (when in reality that projection is not even there)? What I am trying to say that let's just consider one condition for SHM that is force should be proportional to (-) the position of the particle. The original particle doesn't satisfy that then how come its projection experience such force when the force is not even there.
Also I can't really understand if a spring and pendulum same equation of SHM how is possible that they move in different direction and still have same equation (spring moves linearly while pendulum moves parabolically).