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QUESTION 1 Imagine that you have two oscillators with the same amplitude, but different frequencies: X₁ (t) = Acos(wit) and X₂(t) = Acos(w₂t). What happens when you sum these together? Use a trig identity (see PDF under 'Supplementary Texts') to re-express the sum (X₁ + X₂) so that the result looks like (Amplitude)(cos M)(cos N). In other words the result is an amplitude times two cosine terms of "something" (M and N). Once you have this expression, consider the specific case where f₁ = w₁/(2T) = 56 Hz while f2 = w2/(2T) = 54 Hz. Plot X_total versus time and describe what you see. Where do the "M" and "N" parts of the solution figure in? (hint: only plot over the interval x=0,1)

QUESTION 1 Imagine that you have two oscillators with the same amplitude, but different frequencies: X₁ (t) = Acos(wit) and X₂(t) = Acos(w₂t). What happens when you sum these together? Use a trig identity (see PDF under 'Supplementary Texts') to re-express the sum (X₁ + X₂) so that the result looks like (Amplitude)(cos M)(cos N). In other words the result is an amplitude times two cosine terms of "something" (M and N). Once you have this expression, consider the specific case where f₁ = w₁/(2T) = 56 Hz while f2 = w2/(2T) = 54 Hz. Plot X_total versus time and describe what you see. Where do the "M" and "N" parts of the solution figure in? (hint: only plot over the interval x=0,1)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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QUESTION 1 Imagine that you have two oscillators with the same amplitude, but different frequencies: X₁ (t) = Acos(wit) and X₂(t) = Acos(w₂t). What happens when you sum these together? Use a trig identity (see PDF under 'Supplementary Texts') to re-express the sum (X₁ + X₂) so that the result looks like (Amplitude) (cos M)(cos N). In other words the result is an amplitude times two cosine terms of "something" (M and N). Once you have this expression, consider the specific case where f₁ = w₁/(2T) = 56 Hz while f2 = w2/(2T) = 54 Hz. Plot X_total versus time and describe what you see. Where do the "M" and "N" parts of the solution figure in? (hint: only plot over the interval x=0,1)
Transcribed Image Text:QUESTION 1 Imagine that you have two oscillators with the same amplitude, but different frequencies: X₁ (t) = Acos(wit) and X₂(t) = Acos(w₂t). What happens when you sum these together? Use a trig identity (see PDF under 'Supplementary Texts') to re-express the sum (X₁ + X₂) so that the result looks like (Amplitude) (cos M)(cos N). In other words the result is an amplitude times two cosine terms of "something" (M and N). Once you have this expression, consider the specific case where f₁ = w₁/(2T) = 56 Hz while f2 = w2/(2T) = 54 Hz. Plot X_total versus time and describe what you see. Where do the "M" and "N" parts of the solution figure in? (hint: only plot over the interval x=0,1)
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