Question

A vibrating system consists of a mass of 100 kg, a spring of stiffness 50 kN/m and a damper. The damper provided is only 10% of the critical value.

The ratio of two consecutive amplitudes is

• A. 0.98
• B. 1.88
• C. 2.72
• D. 3.66

Answer 1

The correct option is B 1.88

$m=100\text{kg}$

$k=50\text{kN/m}$

$c=0.1c_c$

$\xi =\frac{c}{c_c}=0.1$

$\delta =\frac{2\pi \xi }{\sqrt{1-{\xi }^2}}=\frac{2\pi \times 0.1}{\sqrt{1-(0.1{)}^2}}=0.63$

$\frac{X_n}{X_{n+1}}=e^{\delta }=e^{\left(0.63\right)}=1.88$