Previously, I knew that the spring constant of a spring doesn't depend on the mass of the spring nor the mass of the object attached at the end of the spring.
However, after doing this numerical today, confusions arose in my mind:
We are concerned with 'c':
Now here we see that after attaching objects of different masses to the end of the spring, we are measuring different spring constants of the same spring. How could this be? Is this numerical painting a false picture of the real world?
No, the spring constant of a simple spring doesn't change. Here is what is happening: With zero added mass, the spring is trying to collapse into a shorter length but cannot because the coils are interfering with each other. They are exerting forces, keeping the spring longer than it would be if zero force was acting on each coil. The addition of the 80 g mass in earth's gravitational field is apparently enough to separate the coils. So calculating the spring constant with the first length change gives in inaccurate value.
Adding more mass will (in gravity) will give an accurate value of the force change versus the length change: $$\Delta \vec{F} = -k\Delta \vec{x}$$.
