Equation for underdamped harmonic motion

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SUMMARY

The discussion centers on the equation for underdamped harmonic motion, specifically x(t) = C cos(wt) + D sin(wt). Users explore the relationship between complex conjugates A and B, where A = (g,h) and B = (g,-h). It is established that A + B results in a real number (2g, 0), while A - B yields a complex number (0, 2h). The clarification sought pertains to the condition that if x(t) is real, then A must equal B.

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  • Understanding of complex numbers and conjugates
  • Familiarity with harmonic motion equations
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pinkcashmere
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I found an explanation for the equation of under damped harmonic motion, x(t) = C cos(wt) + D sin(wt), but I was wondering if someone could further explain why:

- "However, if you assume the function x(t) is real, then they are related as A = B
- why is (A-B) is imaginary
 

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If A and B are conjugates, A = (g,h) and B = (g,-h).

A + B = (g,h) + (g,-h) = (2g,0). This is a real number.
A - B = (g,h) - (g,-h) = (0,2h). This is a complex number.
 
spamanon said:
If A and B are conjugates, A = (g,h) and B = (g,-h).

A + B = (g,h) + (g,-h) = (2g,0). This is a real number.
A - B = (g,h) - (g,-h) = (0,2h). This is a complex number.

thanks,
can you also explain the "However, if you assume the function x(t) is real, then they are related as A = B" bit
 

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