Understanding the Relationship

The period (T) of oscillation for a mass-spring system is related to the mass (m) and the spring constant (k) by the following equation:

T = 2π√(m/k)

Solving for the Force Constant (k)

1. Rearrange the equation: To solve for k, we need to isolate it:

k = (4π²m) / T²

2. Plug in the values:

* m = 1 kg (given)

* T = 0.500 s (given)

3. Calculate:

k = (4π²(1 kg)) / (0.500 s)²

k ≈ 158 N/m

Therefore, a force constant of approximately 158 N/m is needed to produce a period of 0.500 seconds for a 1 kg mass.