Simple Pendulum Problem: Finding Coefficient of Linear Expansion

AI Thread Summary
A simple pendulum's string loses 5 seconds per day at 15 degrees Celsius and gains 10 seconds at 30 degrees, prompting a calculation for the coefficient of linear expansion (alpha) of the string's material. The user initially struggled to relate the pendulum's period to its length, given the unknowns of length and temperature change. Guidance was sought on how to connect the time periods and lengths to find alpha. The discussion concluded with the user confirming they understood the relationship and how to proceed with the calculations. The problem highlights the interplay between temperature, time period, and material properties in pendulum mechanics.
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Homework Statement



A simple pendulum whose string is made of some unknown material loses 5 seconds per day at 15 deg and gains 10 seconds at 30 deg. What is the alpha i.e. coefficient of linear expansion of this material?

Homework Equations





3. The Attempt at a Solution [/b

I assumed the length where the pendulum has correct period to be L. Then,

L15(Length at 15 deg)= L-(L*alpha*delta T) where delta T is the fall in temperature but since I do not know both L and delta T, I got stuck. Something similar happens for T =30 deg.

Please guide me.
 
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How is the time period related to the length of the pendulum?
Calculate with the ratio of the time periods and that of the lengths.

ehild
 
Thanks. I got it.
 

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