# Using dimensions to derive an equation

1. Oct 11, 2015

### Darren Byrne

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

3. The attempt at a solution

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

2. Oct 11, 2015

### haruspex

Dimensional analysis works like this. First, express each of the inputs and the output in the form MxLyTz, etc. (so, if electric charge were to feature then there could also be a Qt 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.