Help rearranging this equation.

[dwartenb89]

Homework Statement

On the construction site for a new skyscraper, a uniform beam of steel is suspended from one end. If the beam swings back and forth with a period of 5.00 , what is its length?

I know the equation I need to use but I'm having trouble rearranging it to solve for Length (L).

Homework Equations

T=2pi*sqrt(L/g)*(sqrt2/3)

The Attempt at a Solution

I tried to rearrange the equation to solve for L and got this.
L=sqrt[g*(T/(2pi*sqrt(2/3)))]

any help would be great!

 

[LowlyPion]

Welcome to PF.

Why not simply square both sides of the original?

You know all the other values. Plug them in.

 

[thomate1]

First, let's start by writing the equation in a more standard form:

T = 2π√(L/g) * (√2/3)

Next, we can square both sides of the equation to get rid of the square root on the left side:

T^2 = (2π√(L/g) * (√2/3))^2

Simplifying the right side, we get:

T^2 = 4π^2(L/g) * (2/9)

Now, we can divide both sides by 4π^2 to isolate the term for L:

T^2 / (4π^2) = (L/g) * (2/9)

Finally, we can multiply both sides by g and then divide by (2/9) to solve for L:

L = (T^2 * g) / (4π^2 * 2/9)

This gives us the final equation for L:

L = (9T^2 * g) / (8π^2)

So, the length of the beam can be calculated by plugging in the value for T (period) and g (acceleration due to gravity). I hope this helps with your homework!