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Jason knows that the equation to calculate the period of a simple pendulum is , where T is the period, L is the length of the rod, and g is the acceleration due to gravity. He also knows that the frequency (f) of the pendulum is the reciprocal of its period. How can he express L in terms of g and f?

Respuesta :

Answer:

[tex]L=\dfrac{g}{4\pi^2 f^2}[/tex]

Step-by-step explanation:

The equation to calculate the period of a simple pendulum is: [tex]T=2\pi \sqrt{\frac{L}{g} }[/tex]

Where:

  • T is the period
  • L is the length of the rod; and
  • g is the acceleration due to gravity.

Likewise, Frequency (f) of the pendulum [tex]f=\frac{1}{T}[/tex] therefore [tex]T=\frac{1}{f}[/tex]

We want to express L in terms of g and f.

From

[tex]T=2\pi \sqrt{\frac{L}{g} }[/tex]

[tex]T=\frac{1}{f}[/tex]

[tex]\frac{1}{f}=2\pi \sqrt{\frac{L}{g} }\\$Divide both sides by 2\pi\\\dfrac{1}{2\pi f}=\sqrt{\dfrac{L}{g} }\\$Square both sides\\\left(\dfrac{1}{2\pi f}\right)^2=\dfrac{L}{g}[/tex]

[tex]\dfrac{1}{4\pi^2 f^2}=\dfrac{L}{g} \\$Multiply both sides by g\\Therefore: L=\dfrac{g}{4\pi^2 f^2}[/tex]

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