A spring with a spring constant of 53.0 N/m is attached to different masses, and the system is set in motion. What is its period for a mass of 2.7 kg?
To find the period of the system, we will use the equation for the period of a mass-spring system:
T = 2π√(m/k)
where T is the period, m is the mass, and k is the spring constant.
Given that the spring constant is 53.0 N/m and the mass is 2.7 kg, we can substitute these values into the equation to find the period.
T = 2π√(2.7 kg / 53.0 N/m)
Now, let's simplify the equation step by step:
1. Divide the mass by the spring constant:
T = 2π√(2.7 kg / 53.0 N/m)
= 2π√(0.051 kg·m/N)
2. Take the square root of the resulting value:
T = 2π√(0.051 kg·m/N)
≈ 2π * 0.226
3. Multiply the value by 2π:
T ≈ 2π * 0.226
≈ 1.422 s
Therefore, the period of the system with a mass of 2.7 kg and a spring constant of 53.0 N/m is approximately 1.422 seconds.