Period = 2*pi*sqrt(m/k)
Solve for k.
m/k = [P/(2 pi)]^2
k = ?
Solve for k.
m/k = [P/(2 pi)]^2
k = ?
The formula is:
T = 2π√(m/k)
Given:
Mass (m) = 0.38 kg
Period (T) = 0.63 s
We can rearrange the formula to solve for the force constant (k):
k = (4π²m) / T²
Let's substitute the given values into the formula to find the force constant:
k = (4π² * 0.38 kg) / (0.63 s)²
k = (4 * 3.14159² * 0.38 kg) / (0.63 s)²
k ≈ 23.606 N/m
Therefore, the force constant of the spring is approximately 23.606 N/m.
T = 2π√(m/k)
where T is the period, m is the mass, and k is the force constant of the spring.
Rearranging the equation, we get:
k = (4π²m) / T²
Now we can substitute the given values into the equation:
m = 0.38 kg
T = 0.63 s
k = (4π² * 0.38 kg) / (0.63 s)²
First, let's calculate the denominator:
(0.63 s)² = 0.3969 s²
Now we can substitute this value and the mass into the equation:
k = (4π² * 0.38 kg) / 0.3969 s²
Calculating further:
k = 38.2781 N/m
Therefore, the force constant of the spring is approximately 38.28 N/m.