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]
