Solve for Amplitude and Phase of a Sinusoidal Function | Homework Help

[ecas]

Homework Statement

Find the amplitude and phase of the sinusoid (4√3-3)cos(2t + 30°) + (3√3 – 4)cos(2t + 60°)

Homework Equations

Acos wt + Bsin wt

The Attempt at a Solution

Answer should be amplitude 5 and phase 36.9° but I get 4.11 and 5.7

 

[berkeman]

Homework Statement

Find the amplitude and phase of the sinusoid (4√3-3)cos(2t + 30°) + (3√3 – 4)cos(2t + 60°)

Homework Equations

Acos wt + Bsin wt

The Attempt at a Solution

Answer should be amplitude 5 and phase 36.9° but I get 4.11 and 5.7

Welcome to the PF. Please show us your work, so that we can try to help you. That's how it works here on the PF.

 

[ecas]

The square root of (4√3-3)^2 + (3√3 – 4)^ 2 = 4.11 and θ = tan^-1 (4√3-3)/(3√3 – 4) = 16.9 degrees

 

[berkeman]

The square root of (4√3-3)^2 + (3√3 – 4)^ 2 = 4.11 and θ = tan^-1 (4√3-3)/(3√3 – 4) = 16.9 degrees

Not sure what that's meant to represent. You have two sinusoidal functions of time, which can be added to make a new sinusiodal function, with a combined amplitude, and a combined resultant phase. It should look something like this:

f(t) = A cos(2t + phase)

What would be a way that you can add two cosine functions that have different phases?

 

[berkeman]

Ah, I see the way that you are wanting to solve this:

http://www.cs.sfu.ca/~tamaras/sinusoids318/Adding_two_sinusoids.html

Are you sure you have the original equations in the right format to apply the equations?

 

[ecas]

I tried changing the second function from cos to sin to match the identity but this does not seem to affect the magnitude in any way. I still do not know how to arrive at A=5.

 

[The Electrician]

Does this have anything to do with the study of electronics? If so, have you studied phasor arithmetic yet?

 

[ecas]

Actually the problem comes before the section on phasors. Supposedly it is supposed to be solved with the trig identities we are given.

 

[Redbelly98]

See the link berkeman gave in post #5. You eventually want to get things in the form

A cos(2t) + B sin(2t)​

To do that you'll need to use the addition identity for cosine,

cos(x+y) = ?​

 

[ecas]

Ok I am getting 5.1 which sounds right. Thanks everyone.