Question

Students measure the motion of a pendulum. In one experiment, they release thependulum from a height of 8.65 cm above its lowest point, then observe it as it swingsfive times, and see that this takes 5.87 seconds.What is the length of the pendulum?

Answer 1

Given data

*The given height is 8.65 cm

*The number of oscillation is 5 swings

5 swings take 5.87 second

One swing takes the time period is calculated as

`\begin{gathered} T\text{ =}(5.87)/(5) \\ =1.17\text{ s} \end{gathered}`

The expression for the time period of the pendulum is given as

`T=2\pi\sqrt[]{(L)/(g)}`

*Here L is the length of the pendulum

*Here g is the acceleration due to the gravity

Substitute the values in the above expression as

`\begin{gathered} 1.17=2*3.14\sqrt[]{(L)/(9.81)} \\ L=0.34\text{ m} \\ L=34\text{ cm} \end{gathered}`