Lesson 2: Error Calculations
Equation: T = 2π √(extension/k) ∴ k = 4π2 extension/T2
1. 1. For a 300g mass on a spring, estimate the extension and time period of oscillation to work out its spring constant (k)
esEstimate:
extension = 0.05 m.
T = 1 s.
m = 300 g
∴ k = 4π2 extension/T2
∴ k = 4π2 * 0.05 / (1)2
∴ k = 2 Nm-1 (1 s.f.)
2. Now make some measurements, with uncertainties of T and m
Measurement:
extension = 0.03 m. ± 0.01 m.
T = 0.43 s. ± 0.10 s.
m = 300 g.
What is your calculated value of k? ∴ k = 4π2 extension/T2
∴ k = 4π2 * 0.03 / (0.43)2
∴ k = 2.75 Nm-1