Simple Pendulum Problem: Finding Coefficient of Linear Expansion

[amal]

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.

 

[ehild]

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

 

[amal]

Thanks. I got it.