Hi! I have been racking my brain trying to solve the relationship between the effect of temperature increase and the change in period of a pendulum. I am suppose to prove a relationship, and am given that the relationship is(adsbygoogle = window.adsbygoogle || []).push({});

delta(P) = 1/2*alpha*Pinitial

where alpha is the coefficient of linear expansion with temperature.

We are given that we are dealing with a simple pendulum, so the period is equal to 2*pi*sqrt(L/g)

I know the pendulum length will change under change of temperature to alpha*L*delta(T), for a total new length of L+alpha*L*delta(T)

the change in period then I would guess is:

delta(P) = 2*pi*sqrt((L+alpha*L*delta(T)/g) - 2*pi*sqrt(L/g)

I have tried to simplify this a dozen different ways but I never seem to get the required end formula. I think I can pull out Pinital by dividing everything by 2*pi*sqrt(L/g) to get

delta(P) = Pinitial*(sqrt(1+alpha*delta(T))-1)

but am stuck after that.

thanks for any help!

p.s. is there a summary list for the symbol set this forum uses to generate symbols like pi, square roots etc?

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# Change in Pendulum's Period with temperature.

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