Springs don't include force due to gravity proof

The video tutorial explains why the force of gravity acting on a block connected to a spring does not appear in the final equation of motion. It is not neglected but cancels out mathematically. The tutorial covers the static deflection of a spring with a mass attached, using a free body diagram to illustrate the forces involved. It then explores the dynamic behavior of the spring system when stretched further, leading to the realization that gravity cancels out in the equation, resulting in a simple harmonic motion formula.

How does the equation of motion change when the spring is stretched beyond its static deflection?

What conclusion can be drawn about the role of gravity in the equations of motion for a spring system?