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Question Number 84323 by Rio Michael last updated on 11/Mar/20

$$\mathrm{A}\mathrm{particle}\mathrm{moving}\mathrm{in}\mathrm{a}\mathrm{straight}\mathrm{line}OX\mathrm{has}\mathrm{a}$$$$\mathrm{displacement}x\mathrm{from}O\mathrm{at}\mathrm{time}t\mathrm{where}x\mathrm{satisfies}$$$$\mathrm{the}\mathrm{equation}\frac{d^{2}x}{{dt}^2}+2\frac{dx}{dt}+3x=0$$$$\mathrm{the}\mathrm{damping}\mathrm{factor}\mathrm{for}\mathrm{the}\mathrm{motion}\mathrm{is}$$$$\left[\mathrm{A}\right]e^{-1}$$$$\left[\mathrm{B}\right]e^{-2t}$$$$\left[\mathrm{C}\right]e^{-3t}$$$$\left[\mathrm{D}\right]e^{-5t}$$

Answered by TANMAY PANACEA last updated on 11/Mar/20

$$m\frac{d^{2}x}{{dt}^2}+b\frac{dx}{dt}+kx=0m=1b=2k=3$$$$dampingfactor=e^{\frac{-bt}{2m}}=e^{-\frac{-2t}{2\times 1}}=e^{-t}$$$$$$

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