Practical Design 4 – Linearising Equations

A physics phenomenon can be modelled using an equation.
When the dependent variable is plotted against the independent variable, if a straight line graph is obtained, there is a linear relationship between these two variables.
If the graph is not a straight line, the relationship is non-linear.
We can apply Linear Law to transform a non-linear relationship to a linear form to determine unknown constants from the straight line graph.

Y = mX + c

where,

m = gradient of graph
c = Y-intercept

Example
The period of a pendulum, T, is related to the length, L, of the pendulum by the equation: T = 2π √(L/g) What graph would you plot to verify this equation? To separate L from g we can square both sides of the equation: T² = (4π²L)/g Plotting a graph of T² (y-axis) against L (x-axis) will give a straight line graph with y-intercept at 0 and gradient, m = 4π²/g.

Example

The period of a pendulum, T, is related to the length, L, of the pendulum by the equation:

T = 2π √(L/g)

What graph would you plot to verify this equation?

To separate L from g we can square both sides of the equation:

T² = (4π²L)/g

Plotting a graph of T² (y-axis) against L (x-axis) will give a straight line graph with y-intercept at 0 and gradient, m = 4π²/g.

Physics with Mr Shone