Final answer:
The period of a 509 g mass oscillating on a spring with a spring constant of 25.0 N/m is approximately 0.9 seconds, calculated using the formula T = 2π√(m/k).
Step-by-step explanation:
The period of a mass oscillating on a spring can be calculated using the formula T = 2π√(m/k), where T is the period, m is the mass attached to the spring in kilograms, and k is the spring constant in newtons per meter.
In this case, the mass is 509 g, which we convert to kilograms by dividing by 1000, giving us 0.509 kg. The spring constant is given as 25.0 N/m.
Using the formula, we can find the period:
T = 2π√(0.509 kg / 25.0 N/m)
T = 2π√(0.02036 kg·m/N)
T = 2π√(0.02036)
T = 2π × 0.1427
T ≈ 0.9 seconds (rounded to one decimal place)
Therefore, the period of the mass oscillating on the spring is approximately 0.9 seconds.