The period T (in seconds) of a pendulum is given by t=2pi /root(l/32)

Question

, where L stands for the length (in feet) of the pendulum. If pi=3.14
, and the period is 15.7
seconds, what is the length?

The length of the pendulum is blank feet.

The solution is

Answer 1

To find the length \( L \) of the pendulum given the period \( T = 15.7 \) seconds, we start with the formula for the period:

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

Given \( \pi \approx 3.14 \), we can substitute this value into the equation:

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

We can simplify this to:

\[ T \approx 6.28 \sqrt{\frac{L}{32}} \]

Now we can substitute \( T = 15.7 \):

\[ 15.7 \approx 6.28 \sqrt{\frac{L}{32}} \]

Next, we solve for \( \sqrt{\frac{L}{32}} \):

\[ \sqrt{\frac{L}{32}} = \frac{15.7}{6.28} \]

Calculating the right side:

\[ \sqrt{\frac{L}{32}} \approx \frac{15.7}{6.28} \approx 2.5 \]

Now, squaring both sides gives:

\[ \frac{L}{32} = (2.5)^2 = 6.25 \]

Now, we can solve for \( L \):

\[ L = 6.25 \times 32 \]

Calculating this gives:

\[ L = 200 \text{ feet} \]

Thus, the length of the pendulum is 200 feet.