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Answer :
Using the formula for the period of a simple pendulum, the length of the cable supporting a trapeze artist swinging with a period of 3.8 seconds is approximately 3.47 meters.
To calculate the length of the cable supporting the trapeze swinging with simple harmonic motion and a period of 3.8 s, we use the formula for the period of a simple pendulum:
T = 2π√(L/g)
where T is the period, L is the length of the pendulum (cable, in this case), and g is the acceleration due to gravity (approximately 9.81 m/s² on Earth's surface).
Rearranging the formula to solve for L gives us:
L = (T²g)/(4π²)
Plugging in the values:
L = (3.8² * 9.81 m/s²)/(4 * 3.14²)
L ≈ 3.47 meters
So, the length of the cable supporting the trapeze is approximately 3.47 meters. This calculation assumes the trapeze acts as a simple pendulum and does not take into account factors such as air resistance and the mass of the trapeze artist.
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