leonorapraise leonorapraise
  • 17-07-2022
  • Mathematics
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a simple pendulum of amplitude completes 24 oscillations in one minute. find the length of the string the pendulum bob is attached​

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subtomex0
subtomex0 subtomex0
  • 17-07-2022

[tex]frequency = \frac{24 \: osc}{60 \: sec} = 0.4 \: osc \: per \: sec[/tex]

[tex]period = \frac{1}{frequency} = \frac{1}{0.4} = 2.5 \: sec \: per \: osc[/tex]

[tex]t = 2\pi \sqrt{ \frac{l}{g} } \\ 2.5 = 2\pi \sqrt{ \frac{l}{9.8} } \\ \frac{2.5}{2\pi} = \sqrt{ \frac{l}{9.8} } \\ ( \frac{2.5}{2\pi} ) {}^{2} = \frac{l}{9.8}[/tex]

[tex]l = ( \frac{2.5}{2\pi} ) {}^{2} \times 9.8 = 1.55148 \: meters[/tex]

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