- #1

Nathan B

## Homework Statement

A pendulum shortens due to a change in temperature, decreasing the length L and therefore period T. How many seconds ahead does the clock get in 24 hours? We assume that the grandfather clock is completely accurate at a normal pendulum length.

L

_{i}= 1.3 m

ΔT = -10°C

## Homework Equations

Equation for the period of a pendulum, T = 2π√(L/G)

Equation for change in length due to temperature. ΔL = αL

_{i}ΔT

## The Attempt at a Solution

The new and old periods are relatively easy to calculate.

I've gotten all sorts of approximate values for time off, but I need to be exact. One of several methods that I've tried:

T

_{2}/ T

_{1}= time given by the shortened pendulum/actual time

If we want to examine the results of 24 hours of time passing, we take the number of seconds in 24 hours to be our actual time = 84600 seconds.

Time given by shortened pendulum = 84600*T

_{2}/ T

_{1}

subtract actual time and we know how far off we are:

Time off in seconds = 84600*T

_{2}/ T

_{1}- 84600

This seems like it should work, but it's always a little bit off.

What can I do to make this more accurate?