To find the spring constant, we can use the formula for the period of simple harmonic motion:
T = 2π√(m/k)
Where:
T = period of oscillation
m = mass attached to the spring
k = spring constant
Given that the mass (m) is 0.2 kg and the period (T) is 0.5 s, we can rearrange the formula to solve for the spring constant (k).
Rearranging the formula:
T = 2π√(m/k)
(T/2π)² = m/k
k = m/(T/2π)²
Plugging in the values:
k = 0.2 / ((0.5 / (2π))²)
Calculating the spring constant:
k = 0.2 / ((0.5 / 6.28)²)
k ≈ 1.005 N/m
Therefore, the spring constant (k) is approximately 1.005 N/m.