Relationship of simple pendulum

[joelKID984]

hi guys,

I'm currently working on a physics report about a simple pendulum and can't figure out how to answer one of the questions:

3. "define all terms in the solution(x(t)=Acos(ωt)) and especially the relationship between angular frequency, and periodic time, T."

ive defined all the terms, A is amplitude, ω is angular frequency etc. but have no clue of the relationship between angular frequency, and periodic time?

I know that ω=2∏/T = 2∏f

and

T=2∏√l/g

but don't get their relationship?

any help will be great.

cheers,
Joel C.

 

[rock.freak667]

I know that ω=2∏/T = 2∏f

This is your relationship here.

The other formula you gave just gives the periodic time as a function of length.

 

[joelKID984]

Thanks mate.

So I something like "it can be established that the relationship between angular frequency and period time is:

ω=2∏f"

Do I say anything else? There is 2∏ in both equations, is that some sort of relationship?

Cheers,
Joel

 

[rock.freak667]

Thanks mate.

So I something like "it can be established that the relationship between angular frequency and period time is:

ω=2∏f"

Do I say anything else? There is 2∏ in both equations, is that some sort of relationship?

Cheers,
Joel

The only other relation would be T=2π√(l/g), but generally you can leave it as that.

In the derivation for the periodic time, you get to a point where ω²= g/l and that ω=2π/T as per its definition.