Question

A visitor to a lighthouse wishes to determine the height of the tower. She ties a spool of thread to a small rock to make a simple pendulum, which she hangs down the center of a spiral staircase of the tower. The period of oscillation is 10.1 s. The acceleration of gravity is 9.8 m/s 2 . What is the height of the tower?

Answer 1

To solve this problem we must rely on the equations of the simple harmonic movement that define the period as a function of length and gravity as

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

Where

l = Length

g = Gravity

Re-arrange to find L,

$L = g (\frac{T}{2\pi})^2$

Our values are given as

$g = 9.81m/s$

$T = 10.1s$

Replacing,

$L = g (\frac{T}{2\pi})^2$

$L = (9.81) (\frac{10.1}{2\pi})^2$

$L = 25.348m$

Therefore the height would be 25.348m