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?
Logarithmic decrement is given as \[\delta =\frac{2\pi\xi }{\left ( 1- \xi^{2} \right )^{1/2}}\]
Viscous damping is given as \[\frac{c}{2\sqrt{km}}\]
\[\Rightarrow \delta =\frac{2\pi\times \frac{c}{2\sqrt{km}}}{\left ( 1-\frac{c^{2}}{4km} \right )^{1/2}}
\\=\frac{2\pi c}{\sqrt{4km-c^{2}}}\]
