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Deriving equation to get gradient and intercept

T=2π√((H-d)/g)

If values of T^2 are plotted against d, find the equivalent of the intercept and the gradient.

I'm using the y=mx+c methods and I can't get the correct answers.

Gradient is -4π^2/g
Intercept is 4π^2/g * H

How would I get the answers here ?

Thanks for any help.

Reply 1

uberteknik

Original post by wb25

Get rid of the square root by squaring both sides. Then expand out the brackets on the RHS.

Inspect this expanded eq and compare it with the straight line generic equation:

The question says T² is plotted against d. This tells you immediately that

T² is equivalent to y and d is equivalent to x.

The intercept part (c) will be the part of the RHS that does not have d in it.

The gradient m is the rest of the expression with d in it.