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

`L=(g)/(4\pi^2 f^2)`

Explanation:

The equation to calculate the period of a simple pendulum is:
`T=2\pi \sqrt{(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=(1)/(T)` therefore
`T=(1)/(f)`

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

From

`T=2\pi \sqrt{(L)/(g) }`

`T=(1)/(f)`

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

`(1)/(4\pi^2 f^2)=(L)/(g) \\$Multiply both sides by g\\Therefore: L=(g)/(4\pi^2 f^2)`