A spring with a spring constant of 35.0 N/m is attached to different masses, and the system is set in motion.
What is its period for a mass of 2.4 kg?
Answer in units of s
To calculate the period of a spring-mass system, we can use the formula:
T = 2π√(m/k)
Where:
T is the period (time taken for one complete oscillation),
m is the mass attached to the spring, and
k is the spring constant.
In this case, the spring constant (k) is given as 35.0 N/m, and the mass (m) is 2.4 kg.
Plugging these values into the formula:
T = 2π√(2.4 kg / (35.0 N/m))
To simplify the calculation, we can convert the units by dividing N/m by kg:
T = 2π√(2.4 kg / (35.0 N/kg·m))
Now we can perform the calculation:
T = 2π√(2.4 / 35.0) s
Using a calculator:
T ≈ 2π√(0.068571429) s
T ≈ 2π * 0.261783297 s
T ≈ 1.6449 s
Therefore, the period of the spring-mass system with a mass of 2.4 kg is approximately 1.6449 seconds (s).