Measuring g with Physical Pendulum Time Period (T)

[bon]

Homework Statement

Ok worked out the time period of a physical pendulum (T) to be (in terms of constant a, and variable length x):

T^2 = 4pi (1/2a^2 + x^2)/(gx)

Now asked how i could use a measurement of T(x) to measure g.

Homework Equations

The Attempt at a Solution

I guess i have to vary x and measure T and plot some sort of graph, but given the relation above I can't see what the easiest way to determine g would be...

thanks

 

[rock.freak667]

Normally, if you have to plot a graph to get 'g', you'd try as best as you could to make the equation into the form Y=MX+C.

Eg. T²=4π²(L/g), you write this as T²=(4π²/g)L

So that Y=T² and X=L, plot Y vs. X.

 

[bon]

Thanks but I knew this - I'm just not sure how to do this in this case..

 

[rock.freak667]

$$T^2 = 4 \pi \frac{\frac{1}{2}a^2 + x^2}{(gx)}$$


$$T^2 =\frac{4 \pi}{g} \frac{\frac{1}{2}a^2 + x^2}{x}$$

 

[bon]

Thanks but you still have the x at the bottom..

 

[rock.freak667]

I meant X=((1/2)a²+x²)/x

 

[bon]

Oh rite i see. Thanks