Dimensional analysis

1. Nov 22, 2007

Skeptik101

1. A simple pendulum consists of a light inextensible string AB with length L, with the end A fixed, and a perticle of mass M attatched to B. The pendulum oscillates with period T.

It is suggested that T is proportional to the product of powers of M, L and g. Use dimensional analysis to find this relationship.

2. T = K (l/g)1/2

3. ?? Dont know where to start on this one. some sort of substitution to find the variables, but i dont know how.

2. Nov 22, 2007

Skeptik101

also, i am presuming that little g is the surface gravity, ie, 9.81. I think thats what that represents, but i better check that out first.

3. Nov 22, 2007

Staff: Mentor

Yes, g stands for the acceleration due to gravity. What are its dimension?

4. Nov 22, 2007

Skeptik101

g is in N/Kg i think? is that what you mean by its dimension?

5. Nov 22, 2007

Staff: Mentor

Those are units. By dimensions I mean something independent of particular units. The fundamental dimensions are length (L), mass (M), and time (T). So, how would you express the dimension of g in terms of these quantities?

Last edited by a moderator: May 3, 2017
6. Nov 22, 2007

Skeptik101

Yep, sure did help, they pretty much has this exact question as an example on that page;

so, i basically substitiute dimensions, equate indices and solve.

T = kma Lb gc => T = Ma Lb (LT-2)c

a = 0

-2c = 1 => c = 0.5

b + c = 0 => b = 0.5,

...so T = K (L/G)1/2

I think thats right, cheers.

Last edited by a moderator: May 3, 2017