Question

A trapeze artist swings in simple harmonic motion with a period of 3.8 s. Calculate the length of the cable supporting the trapeze.

Please show as much work as you can, and Thanks :)

Answer 1

As we know that time period of simple pendulum is given as

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

here we know that

`T = 3.8 s`

now from above equation we know that

`T^2 = 4\pi^2((L)/(g))`

now on rearranging the above equation we will have

`L = (gT^2)/(4\pi^2)`

now plug in all data into it

`L = ((9.81)(3.8)^2)/(4\pi^2)`

`L = 3.6 m`

so the length of the cable must be 3.6 m