Question

Common Data Questions:
A uniform rigid slender bar of mass 10 kg, hinged at the left end is suspended with the help of spring and damper arrangement as shown in the figure where K=2 kN/m, C = 500 Ns/m and the stiffness of the torsional spring $K_{\theta }$ is 1 kN/m/rad. Ignored the hinge dimensions.

The damping coefficient in the vibration equation is given by

• A. 500 Nms/rad
• B. 500 N/(m/s)
• C. 80 Nms/rad
• D. 80 N/(m/s)

Answer 1

The correct option is C 80 Nms/rad

Equivalent can be written as :
$I\ddot{\theta }+C_1\dot{\theta }+K_T=0\text{...(i)}$

$C{l}_1^2\dot{\theta }+I\dot{\theta }+K{l}_2^2\theta +K_{\theta }\theta =0\text{...(ii)}$

Comparing equations (i) and (ii)
The damping coefficient in the vibration equation,

$C_T=C{l}_1^2=500(0.4{)}^2=0.16\times 500$

$=80\text{Nms/rad.}$