The equation of motion for a single degree of freedom system with viscous damping is $$4\frac{{{{\text{d}}^2}{\text{x}}}}{{{\text{d}}{{\text{t}}^2}}} + 9\frac{{{\text{dx}}}}{{{\text{dt}}}} + 16{\text{x}} = 0.$$ The damping ratio of the system is
A. $$\frac{9}{8}$$
B. $$\frac{9}{{8\sqrt 2 }}$$
C. $$\frac{9}{{16}}$$
D. $$\frac{9}{{128}}$$
Answer: Option C
This Question Belongs to Mechanical Engineering >> Theory Of Machine
Zeta = c / [2 (m. k)^(1/2)]
= 9 / [ 2(4*16)^(1/2)]
= 9 / 2 (8)
= 9 / 16
Given:
m = 4, c = 9 & s = 16.
Damping factor = (c/cc).
w = sqr of s/m = 2.
cc = 2mw = 2*4*2 = 16.
c/cc = 9/16.
Plz explain it