So if a pendulum driven clock keeps perfect time at a certain temperature, and the temperature is changed, how would you find the amount of time the clock gained or lost in a year? You know the two temperatures, and the coefficient of linear expansion, but that is it.

Question

So if a pendulum driven clock keeps perfect time at a certain temperature, and the temperature is changed, how would you find the amount of time the clock gained or lost in a year?  You know the two temperatures, and the coefficient of linear expansion, but that is it.

mrnood · Answer

do oyu know the formula for the period of a pendulum?

mrnood · Answer

You need to get the RATIO of the period at Temp 1 and Temp 2

The period is related to the length (but not linearly) - get the formula

The length can be assumed to be due to 'linear' expansion - and hence you can find the ratio of length at T2 to length at T1 (You will find that the initial length of the pendulum (L1) cancels from the equation)

Using the formula for period - and the ratio of the the lengths you can work out the ratio of the period at the 2 temperatures, and hence get the change over 1 year.

anonymous · Answer

Okay, Thanks

mrnood · Answer

do oyu have the formula for the period?

anonymous · Answer

Yeah, I was just starting the problem with the wrong formula