Question

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 1

Answer:

$L=\dfrac{g}{4\pi^2 f^2}$

Step-by-step explanation:

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

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 $f=\frac{1}{T}$ therefore $T=\frac{1}{f}$

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

From

$T=2\pi \sqrt{\frac{L}{g} }$

$T=\frac{1}{f}$

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

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