Consider a single degree of freedom spring-mass-damper system with mass, damping and stiffness of m , c  and k respectively. What is the logarithmic decrement of this system?

Consider a single degree of freedom spring-mass-damper system with mass, damping and stiffness of m , c  and k respectively. What is the logarithmic decrement of this system?

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    Logarithmic decrement is given as \[\delta =\frac{2\pi\xi }{\left ( 1- \xi^{2} \right )^{1/2}}\]

    Viscous damping is given as \[\frac{c}{2\sqrt{km}}\]

    \[\Rightarrow \delta =\frac{2\pi\times \frac{c}{2\sqrt{km}}}{\left ( 1-\frac{c^{2}}{4km} \right )^{1/2}}
    \\=\frac{2\pi c}{\sqrt{4km-c^{2}}}\]

     

    Kumar59 Answered on 9th October 2019.
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