A spring with a spring constant of 40.1 N/m is attached to different masses, and the system is set in motion.
What is its period for a mass of 2.8 kg?
To find the period of a mass-spring system, we can use the formula:
T = 2π√(m/k)
Where:
T is the period of the system
m is the mass attached to the spring
k is the spring constant
In this case, the mass (m) is given as 2.8 kg, and the spring constant (k) is 40.1 N/m.
Plugging these values into the formula, we have:
T = 2π√(2.8 kg / 40.1 N/m)
To calculate the numerical value, we can use a calculator:
T ≈ 2π√(0.06982543663990025)
Now, let's calculate it step by step:
1. Convert the square root into decimal form:
√(0.06982543663990025) ≈ 0.264064490522704
2. Multiply it by 2π:
2π x 0.264064490522704 ≈ 1.6583984362377157
So, the period (T) for a mass of 2.8 kg attached to a spring with a spring constant of 40.1 N/m is approximately 1.66 seconds.