Using dimensions to derive an equation

[Darren Byrne]

Homework Statement

The frequency of a simple pendulum depends only on its length and the gravitational field strength. Use dimensions to derive a possible form for the equation for this frequency.

Homework Equations

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Not sure. I was looking at f = 1/T as a starting point and g = F/m

The Attempt at a Solution

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I'm fairy new to physics. This question is in the opening chapter on 'dimensions'. I fairly easily worked my way through the first three questions but this one (the last one) is a little trickier for me. I made an attempt (below) but I'm guessing its wrong.

I started with f = 1 /T since it's the only equation I know currently for frequency.

From there I wrote down the dimensions for frequency as [f] = 1 x T^-1

Now I'm stuck. Since this is the opening chapter I doubt they expect me to know the relationship between gravitational field strength, length and frequency so how do I proceed from here?

I thought perhaps I should find the dimensions for gravitational field strength so used g = F/m

and from there got [g] = LT^-2

I made a stab in the dark then and expressed frequency as f = l / T³

I would appreciate any tips on how a beginner would approach a question like this.

Cheers

 

[haruspex]

Dimensional analysis works like this. First, express each of the inputs and the output in the form M^xL^yT^z, etc. (so, if electric charge were to feature then there could also be a Q^t term, etc.). A force would be MLT^-2.
Next, write an equation in which the output form equals a product of input forms raised to unknown powers. E.g. If you wanted a relationship between a force a mass and an acceleration then you would write (MLT^-2)=(M)^q(LT^-2)^r and solve for q, r.