# A pendulum swings back and forth with a period of 0.5 s. What is the length of the pendulum arm?

Jun 22, 2016

The length of the pendulum arm is $0.06 m .$

#### Explanation:

To determine the length of the pendulum arm, we'll have to use the equation below:

Let's identify our known and unknown variables. We have the period of the pendulum, the acceleration due to gravity has a value of $9.81 \frac{m}{s} ^ \left(2\right)$, and $\pi$ has a value of approximately 3.14. The only unknown variable is L, so let's rearrange the equation to solve for L.

What you want to do first is square both sides of the equation to get rid of the square root:

${T}^{2} = {\left(2 \pi\right)}^{2} \times \frac{L}{g}$

Lets's multiply both sides by $g$ to cancel it out on the right hand side and bring it over to the left hand side:

$g \times {T}^{2} = {\left(2 \pi\right)}^{2} \times L$

Now we divide by $4 {\pi}^{2}$ to get L by itself.

$\frac{g \times {T}^{2}}{4 {\pi}^{2}} = L$

Next we can plug in our known values and solve for L like this:

$\frac{9.81 \frac{m}{\cancel{s}} \times 0.5 {\cancel{s}}^{2}}{4 {\pi}^{2}}$

$L = 0.06 m$