Answer :
To find the length of the trapeze cables, the formula for the period of a simple pendulum (T = 2\pi\sqrt{L/g}) is used, with a 4.0-second period and gravity acceleration of 9.81 m/s^2, resulting in a cable length of approximately 3.936 meters.
To calculate the length of the cables supporting the trapeze, which swings with simple harmonic motion, we can use the formula for the period T of a simple pendulum: T = 2\pi\sqrt{\frac{L}{g}}, where L is the length of the pendulum and g is the acceleration due to gravity. Given that the period T is 4.0 seconds and the acceleration due to gravity g is 9.81 m/s2, we can rearrange the formula to solve for L:
L = \frac{T^2 \times g}{4\pi^2}
Plugging in the values, we get:
L = \frac{(4.0 s)^2 \times 9.81 m/s2}{4\pi^2}
After calculating, the length L is approximately 3.936 meters.
