Equation for underdamped harmonic motion

AI Thread Summary
The discussion centers on the equation for underdamped harmonic motion, specifically the relationship between complex conjugates A and B in the context of real functions. It highlights that when A and B are conjugates, their sum results in a real number, while their difference yields an imaginary component. The query seeks clarification on why assuming x(t) is real leads to A equating to B, emphasizing the implications of this assumption on the resulting equations. The distinction between real and imaginary components in the context of harmonic motion is crucial for understanding the behavior of the system. This exploration of complex numbers in relation to real functions is fundamental in the study of harmonic motion.
pinkcashmere
Messages
17
Reaction score
0
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
 

Attachments

  • question.png
    question.png
    34.4 KB · Views: 373
Mathematics news on Phys.org
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
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Thread 'Six Pencil Puzzle'

Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
View full post »

Similar threads

I Alternating Harmonic Numbers are cool, spread the word!
Replies
4
Views
2K
How to prove that motion is periodic but not simple harmonic?
2
Replies
51
Views
4K
I Solutions to Simple Harmonic Motion second order differential equation
Replies
1
Views
1K
I How to interpret complex solutions to simple harmonic oscillator?
Replies
4
Views
2K
Position and acceleration in simple harmonic motion given velocity
Replies
16
Views
1K
B Correct SHM Equation: Does € Matter?
Replies
11
Views
2K
A Measurement uncertainty due to thermal noise
Replies
4
Views
2K
Zero Amplitude Damped Simple Harmonic Motion with k=0.7s^-1 and f=3Hz
Replies
5
Views
1K
How to Calculate Amplitude Decrease in Damped Harmonic Motion After 10 Cycles?
Replies
3
Views
688
Energy of particle in simple harmonic motion
Replies
13
Views
1K

Hot Threads

Recent Insights

Back
Top