Values of a and b in pendulum equation?

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The discussion focuses on determining the values of a and b in the pendulum period equation, expressed as period=2pi(length/a)^b. By taking the logarithm of the equation, it is transformed into log(T)=log(2pi)+b*log(L/a), which aligns with the slope-intercept form of y=mx+b. The participants suggest rewriting log(L/a) as log(L)-log(a) to facilitate solving for a and b. The final equation becomes log(T)=b*log(L)+log(2pi)-b*log(a), allowing for comparison with the regression line from the experiment. This approach provides a systematic method to extract the values of a and b using the slope and intercept from the log-log graph.
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Ok guys so for my lab report I am given an equation of period=2pi(length/a)^b and through this equation and the slope and y-int of my log-log graph I am suppose to solve for the values of a and b. I know that taking the log of the equation gives me log(T)=log(2pi)+blog(L/a) and this relates to the slope intercept equation of y=mx+b where b is the slope. Therefore I know log(T) is y, blog(L/a) is mx and log(2pi) is b. I just can't figure out how to solve for the values of a and b?
 
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Use that log(L/a)=log(L)-log(a). Write the equation for log(T) as function of log(L).
 
Spread your functions into logT=b*logL+log2π-b*loga. Compare to the regression line y=m*x+n from your experiment ,where b is the slope and log2π-b*loga is the intercept.
 
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