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Answer :
The length of the cable supporting the trapeze artist is 0.62 m, given that the artist swings in simple harmonic motion with a period of 0.5 s.
The formula for calculating the period of a simple harmonic motion is given by:T=2π√l/gwhere T is the time period, l is the length of the string and g is the acceleration due to gravity.Substituting the values given, we have:T = 0.5 s => 2π√l/g = 0.5 squaring both sides, we get:4π²l/g = 0.25=> l = 0.25g/4π²In the case of a trapeze artist, the length of the cable is equal to the length of the string holding the artist. Therefore, substituting g = 9.8 m/s², we have:l = 0.25 x 9.8 / 4π²= 0.62 mThe length of the cable supporting the trapeze artist is 0.62 m, given that the artist swings in simple harmonic motion with a period of 0.5 s.
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