# Find the length, L, in inches for a pendulum to complete a swing that takes one second. Use the formula T= 2`pisqrt(L/384)` Where T represents time in seconds and L represents the length of the...

Find the length, L, in inches for a pendulum to complete a swing that takes one second. Use the formula T= 2`pisqrt(L/384)`

Where T represents time in seconds and L represents the length of the pendulum.

So far I got the equation 1= 6.28`sqrt(L/384)`

I'm not sure what to do next.. any help?

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### 4 Answers

T = 1 sec.

Substitute in the formula:

`T = 2pisqrt(L/384)`

`1 = 2pi sqrt(L/384)`

Divide both sides by `2pi` , so that the radical sign will stay alone at one side.

`1/(2pi) = (2pi sqrt(L/384))/(2pi)`

`1/(2pi) = sqrt(L/384)`

Take the squares of both side to get rid of the radical.

`(1/(2pi))^2 = (sqrt(L/384))^2`

`1/(4(pi)^2) = L/384`

Multiply both sides by 384 so L will be left alone on the right side.

`(1/(4(pi)^2))(384) = (L/384)(384)`

`L=384/(4(pi)^2)`

`L = 96/(pi)^2`

or L = 9.73 inches

`T=2pisqrt(L/384)`

Substitute values and get the square root by itself on the one side by using algebra rules:

`1/(2pi)=sqrt(L/384)`

Now square both sides to get rid of the square root:

`(1/(2pi))^2= L/384`

To get L multiply both sides by 384:

`(1/(2pi))^2 times 384 = L`

`therefore L=9.73 ` in (rounded down to 2 decimal places)

T = 1 sec.

Substitute in the formula:

Divide both sides by , so that the radical sign will stay alone at one side.

Take the squares of both side to get rid of the radical.

Multiply both sides by 384 so L will be left alone on the right side.

or L = 9.73 inches

You were a great help aswell, thanks so much!

Substitute values and get the square root by itself on the one side by using algebra rules:

Now square both sides to get rid of the square root:

To get L multiply both sides by 384:

in (rounded down to 2 decimal places)

Thank you so much!