Vertical spring mass oscillator
Imagine the previous system of a constant spring K and a block of mass m, which approach the conditions of an ideal mass-spring oscillator, with the spring vertically attached to a support and block, in an environment that does not cause resistance to system motion:
We can observe that the point where the body is in balance is:
That is, it is the point where elastic force and weight force cancel each other out. Although the potential elastic energy is not zero at this point, this is considered the starting point of the movement.
Starting from the equilibrium point, by pulling the block, the elastic force will be increased, and since this is a restorative force and we are not considering the energy dissipations, the oscillator must remain in MHS, oscillating between points A and -A, since the resulting force in the block will be:
But since weight does not vary with movement, it can be considered as a constant. Thus, the force varies proportionally to the elongation of the movement, so it is an MHS.
Having its period expressed by: