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October 7th, 2015, 12:39 PM  #1 
Senior Member Joined: Oct 2014 From: EU Posts: 224 Thanks: 26 Math Focus: Calculus  Fundamental period of a composite function
Hi all, I am a little bit confused about determining the fundamental period of a function: $\displaystyle x(t) = \cos\left({2 \pi t\over \sqrt{5}}\right) + 7\sin\left({3\pi t\over\sqrt{125}}\right )$ I solve it as follows: $\displaystyle \begin{aligned} & {2\pi \over {{2 \pi t\over \sqrt{5}}}} = \sqrt{5}\\ & {2\pi \over {{3 \pi t\over \sqrt{5}}}} = {2\sqrt{125}\over 3}\\ & (\sqrt{5}\sqrt{125}){\mathrm {lcm}(1,2)\over \mathrm {gcd}(1,3)} = 2\sqrt{5}\sqrt{125} = 50 \end{aligned}$ But graphing the function seems that I am wrong, and the period seems to be $\displaystyle \approx 22.36$. What am I missing ? Thank you un advance. Last edited by szz; October 7th, 2015 at 01:22 PM. 
October 7th, 2015, 01:24 PM  #2 
Senior Member Joined: Oct 2014 From: EU Posts: 224 Thanks: 26 Math Focus: Calculus 
Solved: $\displaystyle \begin{aligned} & {2\pi \over {{2 \pi t\over \sqrt{5}}}} = \sqrt{5}\\ & {2\pi \over {{3 \pi t\over \sqrt{5}}}} = {2\sqrt{125}\over 3} = {10\sqrt{5}\over 3}\\ & (\sqrt{5}){\mathrm {lcm}(1,10)\over \mathrm {gcd}(1,3)} = 10\sqrt{5} \approx 22.36 \end{aligned} $ 

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