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Question Number 129914 by MrJoe last updated on 20/Jan/21

Commented by MrJoe last updated on 20/Jan/21

Find x(t)​

Answered by Dwaipayan Shikari last updated on 20/Jan/21

$$m\stackrel{..}{x}+b\stackrel{.}{x}+kx=0$$$$x=e^{\lambda t}$$$$m{\lambda }^2+b\lambda +k=0\Rightarrow \lambda =\frac{-b\pm \sqrt{b^2-4mk}}{2m}$$$$x\left(t\right)=\mathrm{\Lambda }{e}^{-\frac{b-\sqrt{b^2-4mk}}{2m}t}+\mathrm{\Phi }{e}^{-\frac{b+\sqrt{b^2-4mk}}{2m}t}$$

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