Final answer:
The period of oscillation for a mass-spring system with a 48kg mass and a spring constant of 12 is calculated using the formula T = 2π√(m/k). The correct period is 4π seconds, which is not listed in the provided options, indicating a possible error in the question.
Step-by-step explanation:
The period of oscillation for a mass-spring system undergoing simple harmonic motion can be calculated using the formula T = 2π√(m/k), where T is the period, m is the mass in kilograms, and k is the spring constant in Newtons per meter (N/m). In this case, the mass m is given as 48 kg and the spring constant k is 12 N/m.
To calculate the period, plug the given values into the formula:
T = 2π√(48/12) = 2π√(4) = 2π(2) = 4π s
Therefore, the period of oscillation is 4π seconds, which is not one of the provided options (a, b, c, or d). It appears there might be a typo or error in the options provided.