A 0.38-kg mass attached to a spring undergoes simple harmonic motion with a period of 0.63 s. What is the force constant of the spring?
Period = 2*pi*sqrt(m/k)
Solve for k.
m/k = [P/(2 pi)]^2
k = ?
To find the force constant of the spring (k), we need to use the formula that relates the period (T) of the simple harmonic motion to the mass (m) and force constant (k) of the spring.
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.
To find the force constant of the spring, we can use the equation for the period of simple harmonic motion:
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.