How Can You Derive the Rate of Rotation for a Pendulum at Sea Level?

[Kee10016]

Homework Statement

The rate of rotation for a pendulum was found for the following locations. Using these data, derive a formula for calculating the rate of rotation for a pendulum at sea level for any location on Earth.
• North Pole = 3600/24 Hr
• Smithsonian, Washington, D.C. = 2260/24 Hr
• Equator = 00 /24 Hr
• California Academy of Sciences (370 46.2’) = 220.50/24 Hr

Homework Equations

n= (360)(sin theta)

The Attempt at a Solution

My teacher said we could use Graphical Analysis, but I don't know why I should use that. Should I try finding the rate of rotation for each location?

Homework Statement

The data from question # 1 indicates that no rotation occurs at the equator. This suggests two models to explain pendulum motion rotation. Explain and diagram each model. Explain how each model can be verified from its visual frame of reference.

Homework Equations

The Attempt at a Solution

Homework Statement

3. Explain and show mathematically that a simple pendulum exhibits simple harmonic motion.

Homework Equations

Is there an equation I can use to figure this out?

The Attempt at a Solution

 

[Carid]

Kee

The only obvious difference between these different locations is their latitude.

So, as suggested by your teacher, plot latitude (0° to 90°) along the X axis of a graph and rotational frequency (0 to 3600) on the Y axis. Put into the four data points and see whether you get a straight line or a curve.

If it's a straight line, bingo, it's a linear dependence on latitude and you should be able to formulate an expression for that quite easily. If it's not a straight line then we'll have to check for dependence on the latitude angle in terms of trigonometic functions (sin,cos,tan,etc..)

BTW are you sure your numbers are correct - 2260 and 220.5 ?

 

[Kee10016]

Sorry it's 226 and 220.5