Question

the period of a pendulum is the time it takes the pendulum to complete one cycle, swinging to and fro. for a pendulum that is l centimeters long, the period t is given by the formula t = 2π√(l/980), where t is in seconds. use a calculator to find the period of a pendulum of length (a) 64 cm; (b) 98 cm; (c) 119 cm. (a) the period of a pendulum of length 64 cm is 1.61 seconds. (do not round until the final answer. then round to the nearest hundredth as needed.) (b) the period of a pendulum of length 98 cm is 1.99 seconds. (do not round until the final answer. then round to the nearest hundredth as needed.) (a) the period of a pendulum of length 119 cm is □ seconds. (do not round until the final answer. then round to the nearest hundredth as needed.)

Explanation:

Step1: Substitute \(L = 119\) into the formula \(T = 2\pi\sqrt{\frac{L}{980}}\)

\(T=2\pi\sqrt{\frac{119}{980}}\)
First, simplify \(\frac{119}{980}=\frac{17}{140}\approx0.1214\)

Step2: Calculate the square - root

\(\sqrt{0.1214}\approx0.3485\)

Step3: Multiply by \(2\pi\)

\(T = 2\pi\times0.3485\)
Since \(\pi\approx3.1416\), then \(T=2\times3.1416\times0.3485\)
\(T = 6.2832\times0.3485\approx2.19\)

Answer:

\(2.19\)