# Simple harmonic oscillators and a pendulum clock.

#### clayton26

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)

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#### PeterO

Homework Helper
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)

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
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.