# Oscillation Period in a Lighthouse? (1 Viewer)

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#### wmrunner24

1. The problem statement, all variables and given/known data

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 10.4 s. The acceleration of gravity is 9.8 m/s^2.
What is the height of the tower?

2. Relevant equations

Ug=mgh
K=1/2mv^2
Fc=$$V^2m/r$$

3. The attempt at a solution

So, I'm pretty much taking a stab at the dark as this is one of the last questions on my Newtonian mechanics final and my teacher has never and refuses to explain oscillation period. Go figure. Is it the time it takes for the object to move from its initial position and back to the same point again?

Anyway, I guess what you would do is use the law of conservation of mechanical energy or some kinematic equation, perhaps one of the circular counterparts, and use the time given to determine the velocity, then use that to solve for the radius with the centripetal force equation? I'm pretty lost overall, so any help is much appreciated.

#### berkeman

Mentor
1. The problem statement, all variables and given/known data

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 10.4 s. The acceleration of gravity is 9.8 m/s^2.
What is the height of the tower?

2. Relevant equations

Ug=mgh
K=1/2mv^2
Fc=$$V^2m/r$$

3. The attempt at a solution

So, I'm pretty much taking a stab at the dark as this is one of the last questions on my Newtonian mechanics final and my teacher has never and refuses to explain oscillation period. Go figure. Is it the time it takes for the object to move from its initial position and back to the same point again?

Anyway, I guess what you would do is use the law of conservation of mechanical energy or some kinematic equation, perhaps one of the circular counterparts, and use the time given to determine the velocity, then use that to solve for the radius with the centripetal force equation? I'm pretty lost overall, so any help is much appreciated.
I believe there is a pretty simple pendulum equation that you can use. Try searching at wikipedia.org for pendulum. Hopefully they also have a derivation of the equation there as well.

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