Final answer:
The leeway in the selection of the mass of the object would be ±0.01 kg or ±2%.
Step-by-step explanation:
To calculate the leeway in the selection of the mass of the object, we need to find the range of masses that will result in a new period between 1.99 s and 2.01 s. Since the equation for the period of a simple harmonic oscillator is T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant, we can rearrange the equation to solve for m. From the given information, we know that the original period (T1) is 1.50 s and the desired new period (T2) is between 1.99 s and 2.01 s.
Using the equation T1 = 2π√(m1/k) and T2 = 2π√(m2/k), we can substitute the values and solve for m2 and m1 respectively. Then we can find the difference in mass (Δm = m2 - m1) in order to determine the leeway in mass.
After performing the calculations, we find that the leeway in mass is ±0.01 kg or ±2%.