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Simple harmonic oscillators and a pendulum clock.

  • Thread starter clayton26
  • Start date
4
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Hey physics forums, this is my first post and frankly I'm having trouble conceptualizing this problem. I know harmonic oscillation is involved, as it is a pendulum. However, I know I have to incorporate g into the s.h.o. equation and I'm not quite sure how to do that. Any help would be greatly appreciated.


1. Homework Statement
A pendulum clock which keeps correct time at a point where g=9.8 m/s^2 is found to lose 10 seconds per day at a higher altitude where the gravitational field now has a new value g(n). What is the numerical value of this g(n)?


2. Homework Equations
This is from the force diagrams I've drawn.
Tcos(theta)-mg=ma(x)
Tsin(theta)=ma(y)

I'm lost. Please help!
 

PeterO

Homework Helper
2,425
46
Hey physics forums, this is my first post and frankly I'm having trouble conceptualizing this problem. I know harmonic oscillation is involved, as it is a pendulum. However, I know I have to incorporate g into the s.h.o. equation and I'm not quite sure how to do that. Any help would be greatly appreciated.


1. Homework Statement
A pendulum clock which keeps correct time at a point where g=9.8 m/s^2 is found to lose 10 seconds per day at a higher altitude where the gravitational field now has a new value g(n). What is the numerical value of this g(n)?


2. Homework Equations
This is from the force diagrams I've drawn.
Tcos(theta)-mg=ma(x)
Tsin(theta)=ma(y)

I'm lost. Please help!
The period of a pendulum with small amplitude - like you find on a clock - is related to the length [which doesn't change] and g [which is changing]
I think this problem is more about proportional or percentage change than re-deriving the formula for a pendulum.
The other trick is to work out whether the clock is running fast or slow in the mountains, and what that says about the pendulum.
 

gneill

Mentor
20,497
2,616
Are you expected to derive the period of a pendulum from first principles, or can you use the (well known) formula directly? It can be found in a few seconds with a web search.
 

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