# Oscillation Period in a Lighthouse?

• wmrunner24
In summary, a visitor to a lighthouse wants to find the height of the tower. She uses a simple pendulum with a period of 10.4 s, and the acceleration of gravity is 9.8 m/s^2. The equations Ug=mgh, K=1/2mv^2, and Fc=V^2m/r may be used, but a simpler pendulum equation can be found on Wikipedia.
wmrunner24

## Homework Statement

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?

## Homework Equations

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

## 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.

wmrunner24 said:

## Homework Statement

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?

## Homework Equations

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

## 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.

I would first clarify that the oscillation period is the time it takes for the pendulum to complete one full swing from its starting point and back again. This is an important concept to understand in order to solve the problem.

Next, I would look at the given information and equations to determine the best approach for solving for the height of the tower. The fact that the thread is attached to a small rock suggests that we can treat it as a simple pendulum, with the thread being the pendulum's length. We can use the equation T=2π√(L/g) to solve for the length of the pendulum, where T is the oscillation period, L is the length of the pendulum, and g is the acceleration of gravity.

Once we have the length of the pendulum, we can use trigonometry to determine the height of the tower. We can set up a right triangle with the pendulum's length as the hypotenuse, the height of the tower as one leg, and the horizontal distance from the center of the spiral staircase to the point where the thread is attached as the other leg. We can then use the Pythagorean theorem to solve for the height of the tower.

In summary, the height of the tower can be determined by using the equation T=2π√(L/g) to solve for the length of the pendulum, and then using trigonometry to solve for the height of the tower.

## 1. What is the oscillation period in a lighthouse?

The oscillation period in a lighthouse refers to the time it takes for the lighthouse to complete one full cycle of its beam of light.

## 2. How is the oscillation period in a lighthouse measured?

The oscillation period in a lighthouse is typically measured using a stopwatch or a specialized instrument called a tachymeter. This device is placed in front of the lighthouse and measures the time between each flash of light.

## 3. What factors can affect the oscillation period in a lighthouse?

The oscillation period in a lighthouse can be affected by a variety of factors, including the design and construction of the lighthouse, the type and power of the light source, and any external factors such as weather or mechanical issues.

## 4. How is the oscillation period in a lighthouse important?

The oscillation period in a lighthouse is important because it allows ships and other vessels to accurately determine their location and navigate safely. It also helps lighthouse keepers and operators to monitor and maintain the proper functioning of the lighthouse.

## 5. Can the oscillation period in a lighthouse change over time?

Yes, the oscillation period in a lighthouse can change over time due to a number of factors, such as changes in the light source, wear and tear on the lighthouse mechanism, or structural changes to the lighthouse itself. Regular maintenance and monitoring is necessary to ensure the accuracy and consistency of the oscillation period.

• Introductory Physics Homework Help
Replies
6
Views
3K
• Introductory Physics Homework Help
Replies
18
Views
3K
• Introductory Physics Homework Help
Replies
11
Views
2K
• Classical Physics
Replies
11
Views
359
• Introductory Physics Homework Help
Replies
2
Views
4K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
8
Views
2K
• Introductory Physics Homework Help
Replies
9
Views
6K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
6
Views
1K