A mass of .24 kg is attached to a spring and is set into vibration with a period of .30 s. What is the spring constant of the spring? Answer in units of N/m
To find the spring constant, we can use the formula 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 period (T) is 0.30 seconds and the mass (m) is 0.24 kg, we can rearrange the formula to solve for the spring constant (k):
k = (4π²m) / T²
Substituting the given values:
k = (4π² * 0.24 kg) / (0.30 s)²
k ≈ 98.94 N/m
Therefore, the spring constant of the spring is approximately 98.94 N/m.
To find the spring constant of the spring, we can use the formula for the period of a mass-spring system:
T = 2π√(m/k)
Where:
T - period of the system
m - mass attached to the spring
k - spring constant
In this case, we are given the period T = 0.30 s and the mass m = 0.24 kg. We want to find the spring constant k.
Rearranging the formula, we have:
k = (4π²m) / T²
Now we can substitute the given values into the equation to find the spring constant:
k = (4π² * 0.24 kg) / (0.30 s)²
k = (4 * 3.14159² * 0.24 kg) / (0.30 s)²
Using a calculator to evaluate the expression, we find:
k ≈ 98.083 N/m
Therefore, the spring constant of the spring is approximately 98.083 N/m.