Theory says the pendulum obeys T = 2π√(L/g). You want a straight-line plot whose slope reveals g. What should you plot?

Physics I / Graphical Analysis and Curve Fitting

Practice question · Multiple choice

Theory says the pendulum obeys $T = 2\pi\sqrt{L/g}$ . You want a straight-line plot whose slope reveals $g$ . What should you plot?

Hints

Square both sides of the law and rearrange it into the shape $y = (\text{slope}) \cdot x$ .
$T^{2} = \frac{4\pi^{2}}{g} L$ : what plays $y$ , what plays $x$ , and what is the slope?

Show the answer

A. $T^{2}$ against $L$ , slope $4\pi^{2}/g$

Why

Linearization turns curve-guessing into line-fitting: plotting $T^{2}$ vs $L$ makes the law a straight line through the origin with slope $4\pi^{2}/g$ . Straight lines are the only shapes the eye, and least squares, can judge reliably.

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Theory says the pendulum obeys T=2πL/gT = 2\pi\sqrt{L/g}T=2πL/g​. You want a straight-line plot whose slope reveals ggg. What should you plot?

Practise Graphical Analysis and Curve Fitting

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Theory says the pendulum obeys $T = 2\pi\sqrt{L/g}$ . You want a straight-line plot whose slope reveals $g$ . What should you plot?