A machine part of mass 195 kg vibrates in a viscous medium D

A machine part of mass 1.95 kg vibrates in a viscous medium. Determine the damping coefficient when a harmonic exciting force of 24.46 N results in a resonant amplitude of 1.27 cm with a period of 0.20 sec.

Solution

As given, at resonance, amplitude X_res = F / (C*w_n) = F*t / (2*pi*C)

Here, F is the exciting force, c is damping coefficient, t is time period and w_n is the natural frequency = sqrt (k/m)

We have,

Mass m = 1.95 kg

Time period t = 0.2 sec

X_res = 1.27 cm = 0.0127 m

F = 24.46 N

0.0127 = 24.46*0.2 / (2*3.14*C)

C = 61.306 N-s/m