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Curve fitting and linearisation
Intermediate
Plot y against a transformed x to get a straight line and read constants.
Experimental data are easier to analyse when plotted so the expected relation becomes a straight line y = mx + c, then slope and intercept give physical constants. For T = 2π√(L/g), plot T² against L: slope = 4π²/g.
Measure T for several lengths, plot T² vs L, and get g = 4π²/slope.
Fit the best line through the points, not the origin or the first and last points, and use error bars.
In more detail
Many relations become straight lines when you plot the right quantities, which makes the constant easy to find. For example, plotting the period squared against length for a pendulum gives a straight line whose slope gives g.
Real-world uses
- Plotting T squared against L for a pendulum to measure the local value of g.
- Fitting a straight line to log data reveals exponential decay constants.
- A physicist plots the square of the period against length for a pendulum, which gives a straight line whose slope reveals the value of g.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
What is linearisation?
Transforming data so the relationship becomes linear, so that a straight-line fit gives the physical constants.
What is a line of best fit?
The line that minimises the total squared distance from the data points, often computed with least squares.
Why is a straight line easier to read than a curve?
Your eye can judge a straight line well, and its slope and intercept directly give the constants in the relationship.
Related topics in Measurement & Math Tools
Taylor series and small angles · Complex numbers and phasors · Graphs and slopes · Logarithmic scales