explain how the period of oscillation of the pendulum of a clock maybe affected by an increase in temperature?

Nifeke

7 years ago

FROM STACK EXCHANGE SEE THIS;

There are many, many factors that affect a pendulum's accuracy. There is a fairly famous pendulum clock in the bell tower of Trinity College, Cambridge, which is the subject of a fair bit of scientific analysis and monitoring (it keeps time to better than one second per month). The "keepers" of the clock wrote a detailed discussion about the factors affecting its accuracy

This tells us about a number of things you have to worry about when you want a really accurate clock:

Length of pendulumAmplitude of motionTemperatureChanges in gravityChanges in air density (humidity, barometric pressure)

and it proceeds to estimate (for that particular clock) the effect these factors might have. The time change per day due to changing length, for example, is given to a very good approximation by

ΔT=TΔL2LΔT=TΔL2L

(this is really just a first order expansion of the "exact" expression which ROIMaison gave in his answer). So if you estimate the change in length (coefficient of thermal expansion times temperature change) you can get the change in "going" (seconds lost or gained per day) directly from the above expression.

The Trinity clock has all kinds of compensation mechanisms: a barometric compensator, thermal expansion correction, etc. Incidentally the mechanism for a thermally compensated pendulum is quite ingenious: looking at figure 4 from the above link we see



The "down" rods have one coefficient of thermal expansion and the "up" rods have another: by carefully choosing their relative lengths as a function of this coefficient, it is possible to make it so that the bob remains at a constant distance below the pivot.

Any number of things can give rise to changes in the accuracy of your clock - the change in temperature can change the friction and thus the amplitude as well as the length, to give just one example; I hope that after reading the linked document you will have a better appreciation of the ingenuity of clock makers and the problems they face.

Further links worth reading:

About the Trinity College clock
About the Trinity College clock monitoring project
Wikipedia entry about pendulum clock

best of God.