Question

A trapeze artist swings in simple harmonic motion with a period of 3.8 s

Answer 1

i guess the problem is asking for the length of the cable.

the system can be assimilated to a simple pendulum, whose period is given by:

`T=2 \pi \sqrt{ (L)/(g) }`
where L is the length of the cable and g=9.81 m/s^2.

By re-arranging the formula and using T=3.8 s, we find the length of the cable:

`L= (T^2)/((2 \pi)^2) g = ((3.8 s)^2)/((2 \pi)^2) (9.81 m/s^2)=3.6 m`