**Answer:**

varying the displacement of the mass from its equilibrium position

increasing the amount of time the oscillating system is observed

keeping track of the precise position of the mass through time

**Explanation:**

The period of a mass-spring system is given by:

where

m is the mass hanging from the spring

k is the spring constant

As we can see from the formula, the period depends only on these two factors: mass and spring constant, and nothing else. Therefore, the following factors do not affect the period of the system:

**varying the displacement of the mass from its equilibrium position
**

**increasing the amount of time the oscillating system is observed
**

**keeping track of the precise position of the mass through time**