Question

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?

Answer 1

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:

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