Question

Consider a mass-spring system. The spring has a constant k = 8 N/m and the mass m = 5 kg. The mass oscillates with an amplitude of 7 cm and follows the equations of motion in the introduction. What is the period of oscillation of the mass-spring system?

1) 2�� seconds
2) �� seconds
3) ��/2 seconds
4) 2 seconds

Answer 1

The period of oscillation for the given mass-spring system with a spring constant of 8 N/m and a mass of 5 kg is approximately 2π seconds, which is close to 6.28 seconds.

The correct option is option 1.

Step-by-step explanation:

The student is asking about the period of oscillation for a mass-spring system. To find the period of a mass-spring oscillator, we use the formula T = 2π√(m/k), where T is the period in seconds, m is the mass in kilograms, and k is the spring constant in Newtons per meter.

Given that the spring constant k is 8 N/m and the mass m is 5 kg, we can plug these values into the formula to find the period:

T = 2π√(5 kg / 8 N/m) = 2π√(0.625) ≈ 2π√(0.625) ≈ 2π(0.79) ≈ 2π seconds, which is approximately 6.28 seconds. So the correct answer is option 1.

The correct option is option 1.