Question

A pendulum in the service shaft of a building is used by a physics class for experiments. The shaft is dark, and the top of the pendulum cannot be seen. The bob of the pendulum is visible, and it is observed to complete 13 oscillations in 112 s .Assume g = 9.81 m/s2.
Part A

What is the length of the pendulum?

Answer 1

Answer:

18.4 m

Explanation:

The period of a simple pendulum is given by the equation

$T=2\pi \sqrt{\frac{L}{g}}$ (1)

where

L is the length of the pendulm

g is the acceleration due to gravity

In this problem, we know that:

N = 13 is the number of oscillations completed by the pendulum

t = 112 s is the time taken to complete those oscillations

So the frequency of the pendulum is:

$f=\frac{N}{t}=\frac{13}{112}=0.116 Hz$

The period is the reciprocal of the frequency, so for this pendulum:

$T=\frac{1}{f}=\frac{1}{0.116}=8.62 s$

Now we can use eq(1) to find the length of the pendulum. We know that

$g=9.8 m/s^2$

Therefore, re-arranging the equation for L, we find:

$L=(\frac{T}{2\pi})^2g=(\frac{8.62}{2\pi})^2 (9.8)=18.4 m$