Question

The equation of motion of a spring-mass-damper system is given by
$\frac{d^{2}x}{d{t}^2}+3\frac{dx}{dt}+9x=10sin\left(5t\right)$
The damping factor for the system is

• A. 0.25
• B. 2
• C. 0.5
• D. 3

Answer 1

The correct option is C 0.5

$\frac{d^{2}x}{d{t}^2}+3\frac{dx}{dt}+9x=10sin\left(5t\right)$

Compared with the standard equation:

$\ddot{x}+\left(2\xi {\omega }_n\right)\dot{x}+\left({\omega }_n^2\right)x=\left(\frac{F_0}{m}\right)sin\omega t$

$2\xi {\omega }_n=3$ $$\left[\begin{array}{c}{\omega }_n^2=9\\ {\omega }_n=3\end{array}\right]$$
$2\xi \times 3=3$

$\xi =\frac{1}{2}=0.5$