How to find the frequency of F(t)? I have calculated it numerically and it seems that F(t) also has

Esmeralda Lane 2022-07-07 Answered
How to find the frequency of F(t)? I have calculated it numerically and it seems that F(t) also has a frequency of 2 π, but how to prove it mathematically?
F ( t ) = c 1 sin ( 2 π t ) + c 2 cos ( 2 π t )
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Answers (1)

verzaadtwr
Answered 2022-07-08 Author has 17 answers
If you know Euler's formula, then you can do:
c 1 cos ( ω t ) + c 2 sin ( ω t ) = c 1 cos ( ω t + 0 ) + c 2 cos ( ω t π / 2 ) = R ( c 1 e i ω t ) + R ( c 2 e i ω t i π / 2 ) = R ( c 1 e i ω t + c 2 e i ω t i π / 2 ) = R ( e i ω t ( c 1 + c 2 e i π / 2 ) ) = R ( e i ω t M e i Q ) = R ( M e i ω t + Q ) = M cos ( ω t + Q )

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