A mass of 0.38 kg is attached to a spring and is set into vibration with a period of 0.22 s. What is the spring constant of the spring?
To find the spring constant of the spring, we can use the formula:
Period (T) = 2 * π * √(m / k),
where T is the period of vibration, m is the mass attached to the spring, and k is the spring constant.
Given:
- Mass (m) = 0.38 kg
- Period (T) = 0.22 s
We can rearrange the formula to solve for the spring constant (k):
k = (4 * π² * m) / T²
Substituting the values into the formula:
k = (4 * π² * 0.38) / (0.22)²
Calculating:
k = (4 * 3.14159² * 0.38) / (0.22)²
k ≈ 48.5 N/m
Therefore, the spring constant of the spring is approximately 48.5 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 = period of vibration (given as 0.22 s)
m = mass of the object (given as 0.38 kg)
k = spring constant (unknown)
Now, let's rearrange the formula to solve for k:
k = (4π²m) / T²
Substituting the given values:
k = (4π² * 0.38 kg) / (0.22 s)²
Calculating the expression:
k ≈ 135.6 N/m
Therefore, the spring constant of the spring is approximately 135.6 N/m.
Use this formula to solve for the spring constant k (in Newtons per meter):
P = 2 pi sqrt(M/k)
You know P amd M. Solve for k