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Write y(t) = e-2t (-√3 cos 6t+ sin 6t) as a shifted/scaled form A(t) cos (wt + 8). What are the values cosine wave, i.e., in the of A(t), w and 8?

Write y(t) = e-2t (-√3 cos 6t+ sin 6t) as a shifted/scaled form A(t) cos (wt + 8). What are the values cosine wave, i.e., in the of A(t), w and 8?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.5: Applications
Problem 17EQ
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1. Write y(t) = e-2t (-√3 cos 6t+ sin 6t) as a shifted/scaled cosine wave, i.e., in the form A(t) cos (wt + 8). What are the values of A(t), w and 8? 2. Suppose you have an LC circuit consisting of an inductor L = 0.1H and a capacitor C= 0.001F. If this circuit is connected to a voltage source of frequency w = 108 rad/s, then what is the mean frequency of the resulting oscillations? What about the beat frequency? 4 s
Transcribed Image Text:1. Write y(t) = e-2t (-√3 cos 6t+ sin 6t) as a shifted/scaled cosine wave, i.e., in the form A(t) cos (wt + 8). What are the values of A(t), w and 8? 2. Suppose you have an LC circuit consisting of an inductor L = 0.1H and a capacitor C= 0.001F. If this circuit is connected to a voltage source of frequency w = 108 rad/s, then what is the mean frequency of the resulting oscillations? What about the beat frequency? 4 s
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