The period T (in seconds) of a pendulum is given by T=2pi (sqrt)(L)/32

, where L stands for the length (in feet) of the pendulum. If pi=3.14
, and the period is 6.28
seconds, what is the length?

1 answer

To find the length \( L \) of the pendulum given the period \( T = 6.28 \) seconds, we can start from the formula:

\[ T = 2\pi \sqrt{\frac{L}{32}} \]

We can substitute \( \pi \) with \( 3.14 \):

\[ T = 2 \times 3.14 \sqrt{\frac{L}{32}} \]

Now we can set this equal to the given period:

\[ 6.28 = 2 \times 3.14 \sqrt{\frac{L}{32}} \]

Calculating \( 2 \times 3.14 \):

\[ 2 \times 3.14 = 6.28 \]

Now we have:

\[ 6.28 = 6.28 \sqrt{\frac{L}{32}} \]

To isolate \( \sqrt{\frac{L}{32}} \), we can divide both sides by \( 6.28 \):

\[ 1 = \sqrt{\frac{L}{32}} \]

Now, squaring both sides gives:

\[ 1^2 = \left(\sqrt{\frac{L}{32}}\right)^2 \]

This simplifies to:

\[ 1 = \frac{L}{32} \]

To solve for \( L \), we multiply both sides by \( 32 \):

\[ L = 32 \]

Therefore, the length \( L \) of the pendulum is:

\[ \boxed{32 \text{ feet}} \]