Three pendulums with strings of the same length and bobs ofthe same mass are pul

Question

Three pendulums with strings of the same length and bobs ofthe same mass are pulled out to angles1  ,2 ,3 Respectively and released. Theapproximation sin() = holds for all three angles, with3 < 2 < 1. How do the angular frequencies of the three pendulumscompare? A.) 3<2<1 B.) Need to know the amplitude to answer C.) 1 = 2 = 3 D.) 1>2>3 E.) Need to know g/L to answer Three pendulums with strings of the same length and bobs ofthe same mass are pulled out to angles1  ,2 ,3 Respectively and released. Theapproximation sin() = holds for all three angles, with3 < 2 < 1. How do the angular frequencies of the three pendulumscompare? A.) 3<2<1 B.) Need to know the amplitude to answer C.) 1 = 2 = 3 D.) 1>2>3 E.) Need to know g/L to answer

Explanation / Answer

    When Sin = , then ' ' isvery small.     Time period, T = 2 ( L / g )     Angular frequency, = 2 / T                                     = ( g / L )     The angular frequency is independent of theangle .     As the length is same in all cases , the angularfrequency remains constant.     Ans: Option C : 1 = 2 = 3

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