1. Find the spring constant (k):

* We know the force (F) and the displacement (x) of the spring. Use Hooke's Law:

* F = kx

* k = F/x = 40.1 N / 0.251 m = 159.76 N/m

2. Use the period of oscillation to find the mass (m):

* The period (T) of a mass-spring system is given by:

* T = 2π√(m/k)

* Rearrange the equation to solve for mass (m):

* m = (T² * k) / (4π²)

* Substitute the known values:

* m = (1.06 s² * 159.76 N/m) / (4π²)

* m ≈ 1.44 kg

Therefore, a mass of approximately 1.44 kg must be suspended from the spring to achieve an oscillation period of 1.06 seconds.