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

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

Solution-

The equation for time period of a simple pendulum is given by,

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

Where,

T = Time period,

L = Length of the rod,

g = Acceleration due to gravity.

Frequency (f) of the pendulum is the reciprocal of its period, i.e

`f=(1)/(T)\ \Rightarrow T=(1)/(f)`

Putting the values,

`\Rightarrow (1)/(f)=2\pi \sqrt{(L)/(g)}`

`\Rightarrow ((1)/(f))^2=(2\pi \sqrt{(L)/(g)})^2`

`\Rightarrow (1)/(f^2)=4\pi^2 (L)/(g)`

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

Answer 2

1/f = 2π√(L/g)
1/(2πf) = √(L/g) . . . . . divide by 2π
1/(2πf)^2 = L/g . . . . . .square both sides
g/(2πf)^2 = L . . . . . . .multiply by g

L = g/(4π^2f^2) . . . . . . . matches the 1st selection