How does thermal expansion affect the accuracy of a pendulum clock?

1 Answer
May 26, 2018

the clock will become slower by a small amount due to expansion


A pendulum clock has the Time Period

#T = 2.pi. sqrt ( l/g) # where l= length of the pendulum and g the acceleration due to gravity.

By thermal expansion the length of the pendulum will increase say by a small amount #delta(l)#

so the new time period # T' = 2.pi. sqrt {( l +delta (l) )/g) }#

so, #(T') / T# = # sqrt{( l + delta (l)) /sqrt ( l)}#

or #((T') -T ) /T # = #{ sqrt (1 + delta (l)) - sqrt(l)} / sqrt (l) #

so the time period of oscillation will increase , thereby the clock will give time as if slow by (T'-T)

In clocks people use seconds pendulum whose time period os 2 secs and length is about 1m and if the length increases to say 1.001 m

then T'- T = 2 s . {sqrt ( 1.001)- 1 }

so the error can be estimated.