# Pendulum clock question

1. Sep 8, 2004

### squanto

I am trying to solve this question..

A pendulum clock with a pendulum made of brass is designed to keep accurate time at 23 °C. If the clock operates at 0.0°C, what is the magnitude of its error, in seconds per hour (use a minus sign to indicate slowing down)? The linear expansion coefficient of brass is 19 x 10-6 /C°.

I know that the the period of oscillation is

T= 2pi * sqrt( L /g)

and that the change in the length of the pendulum
is

-4.37E-4 m

I just don't know how to relate the two to solve
Any help is appreciated.

2. Sep 8, 2004

### Tide

Because T varies as the square root of L the relative errors are related by
$$\frac {\delta T}{T} = \frac {1}{2} \frac {\delta L}{L}$$