Straighten the curve, read off g

Plot pendulum data as T² against L and fit a line to measure g.

Interactive

your slope3.5s²/m

g from your line11.28m/s²

best-fit g9.82m/s²

Plot

Slope of your line3.5 s²/m

The math, with your numbers

T = 2\pi\sqrt{\frac{L}{g}} \;\Rightarrow\; T^2 = \frac{4\pi^2}{g}\,L \qquad (y = m\,x)

g = \frac{4\pi^2}{\text{slope}} = \frac{39.48}{3.5} = 11.28\ \text{m/s}^2

Squaring the period turned a curve into a line. Its slope, not any single point, carries the physics.

Try this

→In the T² view, find the steepest and the shallowest lines that still pass through every error bar. What range of g do they give?
→Why is it easier to judge a straight line by eye than a curve?
→Press Best fit. How close is it to 9.81 m/s²?

Want to know why it behaves like this?

The lesson “Best-Fit Lines & Straightening Curves” explains it step by step: How do you find a law of nature hidden in messy data?

Straighten the curve, read off g

Plot pendulum data as T² against L and fit a line to measure g.

Straighten the curve, read off g

Interactive

your slope3.5s²/m

g from your line11.28m/s²

best-fit g9.82m/s²

Plot

Slope of your line3.5 s²/m

The math, with your numbers

T = 2\pi\sqrt{\frac{L}{g}} \;\Rightarrow\; T^2 = \frac{4\pi^2}{g}\,L \qquad (y = m\,x)

g = \frac{4\pi^2}{\text{slope}} = \frac{39.48}{3.5} = 11.28\ \text{m/s}^2

Squaring the period turned a curve into a line. Its slope, not any single point, carries the physics.

Try this

→In the T² view, find the steepest and the shallowest lines that still pass through every error bar. What range of g do they give?
→Why is it easier to judge a straight line by eye than a curve?
→Press Best fit. How close is it to 9.81 m/s²?

Want to know why it behaves like this?

The lesson “Best-Fit Lines & Straightening Curves” explains it step by step: How do you find a law of nature hidden in messy data?