Stitz-Zeager_College_Algebra_e-book

Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: + π 3 y = 10e−x/5 sin x + π 3 , y = ±10e−x/5 √ 2. Proceeding as in the first example, we factor out (t + 3) 2 from each term in the function √ √ √ x(t) = (t + 3) 2 cos(2t) + (t + 3) 2 sin(2t) to get x(t) = (t + 3) 2(cos(2t) + sin(2t)). We find 15 Take a good Differential Equations class to see this! 756 Applications of Trigonometry √ (cos(2t) + sin(2t)) = 2 sin 2t + π , so x(t) = 2(t + 3) sin 2t + π . Graphing this on the 4 4 calculator as y = 2(x + 3) sin 2x + π , we find the sinusoid’s amplitude growing. Since our 4 amplitude function here is A(x) = 2(x + 3) = 2x + 6, which continues to grow without bound as x → ∞, this is hardly surprising. The phenomenon illustrated here is ‘forced’ motion. That is, we imagine that the entire apparatus on which the spring is attached is oscillating as well. In this case, we are witnessing a ‘resonance’ effect – the frequency of the external oscillation matches the frequency of the motion of the object on the spr...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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