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.

 

[PJC01]

Hello Joel,

The relationship between angular frequency (ω) and periodic time (T) is an important concept in understanding the motion of a simple pendulum. The angular frequency represents the rate at which the pendulum swings back and forth, while the periodic time is the time it takes for the pendulum to complete one full swing.

The relationship between these two quantities can be described using the equation ω=2∏/T, where ω is the angular frequency and T is the periodic time. This means that the angular frequency is equal to 2∏ divided by the periodic time.

In other words, the angular frequency is inversely proportional to the periodic time. This means that as the angular frequency increases, the periodic time decreases and vice versa. This relationship can also be seen in the equation T=2∏√l/g, where l is the length of the pendulum and g is the acceleration due to gravity.

This equation shows that the periodic time is directly proportional to the square root of the length of the pendulum and inversely proportional to the square root of the acceleration due to gravity. This means that as the length of the pendulum increases, the periodic time also increases and as the acceleration due to gravity increases, the periodic time decreases.

I hope this helps clarify the relationship between angular frequency and periodic time in a simple pendulum. If you have any further questions, please don't hesitate to ask. Good luck with your report!