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?

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 periodL 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]