Hey guys, I'm having some trouble with an assignment. I need to add a couple of sin voltages, and am having trouble finding out how to do so. So just for example, if I wanted to add 12sin(3t-25degrees) + 17sin(5t-40degrees) I have searched the forums and haven't found a similar topic, But i do apologize if this is a repost of some other thread. Thanks
You need the transformation sin A + sin B = 2 sin 0.5(A + B) cos 0.5 (A - B) followed by a bit of algebraic/trigonometric manipulation to simplify.
I tried got a little stumped on it again, What do I do with the 12 and 17? And for the A and B, for A+B would I just do (3t+5t)+(-25-40) to equal 8t-55? Thanks btw, when I entered it into excel it gave me error.
Just to make sure, would the answer to my equation would be 204Sin(4t-75degrees)Cos(1t+15deegrees)? I would hope that you dont half the phase angle, but correct me if Im wrong. Thanks
Doesn't look correct. Perhaps you could show your derivation. As far as using excel you would just set up column A for the time variable - say from 0 to 7 seconds with a step size of say .05 sec. I'd assume you'd put a heading in row 1 and data would be in row2 onwards Then type the equation in the first column B data cell (i.e. starting at B2) in the form =12*sin(3*A2-25*pi()/180)+17*sin(5*A2-40*pi()/180) then copy down the column to the end of the time data in column A. If you create a similar column for your derived function and plot the data for both cases you'll see something is wrong.
I've actually been looking at this type of problem at work. As far as I can tell the identity studiot posted does not take into account the coefficients 12 and 17. This link should have some information to help you, but it may not be the method your instructor intended. http://scipp.ucsc.edu/~haber/ph5B/addsine.pdf
I'd like to reword the OP's question as: Does anyone know if there's a closed-form expression for (1) where a, x, and y are real numbers that is similar in form to (2) I did a little work looking through some handbooks (CRC Math Tables, Gradshteyn and Ryzhik, "Tables of Integrals, Series, and Products") and looked at Wolfram's Mathworld, but failed to find anything relevant. I also did some numerical experimentation to get a feel for the behavior of the equation for a few choices of the parameters. The reason it would be nice is that formula 2 shows you that the addition of two sinusoids with different frequencies will result in a sinusoid with a frequency that is the difference of the two frequencies (the "beat" frequency) and modulated by a sinusoid that is the sum of the two frequencies. A formula for 1 should reduce to 2 when a = 1. We've been adding sinusoids for hundreds of years and I expect if there was a relatively simple closed form formula for 1, it would be in the math handbooks. But it never hurts asking...
I have to admit I rushed and didn't see the coefficients. If you expand AsinB in a series and sinC in another similar series you can add term by term to get AsinB + sinC = { (AB+C) - (AB^3+C^3)/3! + (AB^5+C^5)/3! - (AB^7+C^7)/7!.....}
Why not just resolve each value first and then add? This is what makes the superposition theorem so super! eric
Thanks for all your help, I found out in class that I was taking this too far, I read the question correctly, however the prof only wanted us to put a plus sign between the two. Hopefully I will get extra credit for this. I even brought this up to my buddy who is a physics major, and he had no clue what to do, however his friend, who is a music theory major helped me to get it. He gave me the same formula as someonesdad Thanks for your help