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Verify that the exponentially damped sinusoid $$y(t)=e^{-3 t} \sin (\sqrt{3} t)$$ is a solution to equation (3) if $$F_{\mathrm{exx}}(t)=0, m=1, b=6$$, and $$k=12$$. What is the limit of this solution as $$t \rightarrow \infty ?$$
$-6 \sqrt{3} e^{-3 t} \cos (\sqrt{3} t)+6 e^{-3 t} \sin (\sqrt{3} t)+6 \sqrt{3} e^{-3 t} \cos (\sqrt{3} t)-18 e^{-3 t} \sin (\sqrt{3} t) )+12 e^{-3 t} \sin (\sqrt{3} t)=0$
Calculus 2 / BC
Chapter 4
Linear Second-Order Equations
Section 1
Introduction: The Mass-Spring Oscillator
Differential Equations
Oregon State University
University of Michigan - Ann Arbor
University of Nottingham
Idaho State University
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