Combination of 2 formulas for a graph

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SUMMARY

The discussion focuses on combining two waveform formulas, specifically 𝑉𝑐 = 4cos(2𝜋125x10^3t) and 𝑉𝑎 = 2cos(2𝜋10x10^3t), to create a third output for analysis. The user seeks to plot these waveforms and understand the resulting modulation, which is identified as amplitude modulation (AM). Key insights include the need to correctly apply trigonometric identities and the importance of adjusting the time scale in graphing software like Desmos to visualize the signals effectively.

PREREQUISITES
  • Understanding of waveform equations and trigonometric identities
  • Familiarity with amplitude modulation (AM) concepts
  • Experience using graphing tools such as Desmos
  • Knowledge of LaTeX for mathematical representation
NEXT STEPS
  • Learn how to use trigonometric identities to combine waveforms effectively
  • Explore the principles of amplitude modulation in depth
  • Practice plotting complex waveforms in Desmos with appropriate scaling
  • Investigate the frequency components of modulated signals and their implications
USEFUL FOR

Electrical engineers, signal processing specialists, and students studying communications who are interested in waveform analysis and modulation techniques.

  • #31
leejohnson222 said:
I would say number 3 and 4 are correct
No.

We are told x = (a+b)c.

We can choose any values we want for a, b and c. For example, suppose a= 1, b =2 and c = 5.

We can put the chosen values in so that we know what x is for our chosen values of a, b and c;
x = (a+b)c = (1+2)*5 = 3*5 = 15

Choice 3) is x = (a+c)b. This gives x = (1+5)*2 = 6*2 = 12. That’s not equal to 15! So choice 3) is wrong.

There is only one correct answer, choice 4), x = ac + bc = 1*5 + 2*5 = 5+10 = 15.

This is very basic maths. If you are on some sort of course which requires maths, you need to do some revision/catching-up. There’s plenty of online stuff available, for example BBC Bitesize Maths. Good luck.
 
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  • #32
i appreaciate your assistance, yes i am on a course after a 15 year break from maths, and i know some of the basic rules are letting me down, with brackets etc, i actually did exactly this by substituing for numbers and went to work out all of the ones your wrote up, problem is its hard after a 10 hour day and sorting the kids out, anyway no excuse i need to improve here to progress. thanks again
 

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