Question

a pendulum is l meters long. the time, t, in seconds that it takes to swing back and forth once is given by t = 2√l. suppose the pendulum takes 4.64 seconds to swing back and forth once. what is its length?
carry your intermediate computations to at least four decimal places, and round your answer to the nearest tenth.

Explanation:

Step1: Start with the formula

We know the formula for the time period of a pendulum is \( t = 2\sqrt{L} \), and we are given \( t = 4.64 \) seconds. We need to solve for \( L \). First, divide both sides of the equation by 2:
\( \frac{t}{2}=\sqrt{L} \)
Substituting \( t = 4.64 \), we get \( \frac{4.64}{2}=\sqrt{L} \), so \( 2.32=\sqrt{L} \).

Step2: Square both sides to solve for L

To isolate \( L \), we square both sides of the equation \( 2.32=\sqrt{L} \). Squaring the left side: \( (2.32)^2 = L \). Calculating \( 2.32\times2.32 \):
\( 2.32\times2.32 = 5.3824 \) (we carried the computation to four decimal places as required).

Answer:

\( 5.4 \) (rounded to the nearest tenth)