Question

In a damped spring-mass system, if the mass is halved and the spring stiffness is doubled, the logarithmic decrement is

• A. unchanged
• B. halved
• C. quadrupled
• D. doubled

Answer 1

The correct option is A unchanged

$\delta =\frac{2\pi \xi }{{\sqrt{1-\xi }}^2}$

$\xi =\frac{C}{2\sqrt{sm}}$

${\xi }^{\prime }=\frac{C}{2\sqrt{s^{\prime }{m}^{\prime }}}=\frac{C}{2\sqrt{2s\frac{m}{2}}}$

$\Rightarrow {\xi }^{\prime }=\xi$
$\Rightarrow \delta =unchanged$