Here's how to calculate the force constant (k) needed for a spring-mass system to have a period of 0.500 s with a mass of 0.0150 kg:

Understanding the Relationship

The period (T) of oscillation for a spring-mass system is determined by the following equation:

T = 2π√(m/k)

where:

* T is the period (in seconds)

* m is the mass (in kilograms)

* k is the spring constant (in Newtons per meter)

Solving for k

1. Rearrange the equation to solve for k:

k = (4π²m) / T²

2. Plug in the given values:

k = (4π²(0.0150 kg)) / (0.500 s)²

3. Calculate the result:

k ≈ 2.37 N/m

Therefore, a force constant of approximately 2.37 N/m is needed to produce a period of 0.500 s for a 0.0150-kg mass.