Question 2.5: Consider a SDOF system shown in Figure 2.2. It undergoes und...
Consider a SDOF system shown in Figure 2.2. It undergoes underdamped free vibrations. The mass = 40 kNs²/m, stiffness k = 3750 kN/m and c = 50 kNs/m. The initial conditions are given as: x(0) = 0.01 m, \dot{x}(0) = 0.1 m/s. Plot the inertia, damping and spring forces.
Mass m = 40 kN s²/m
Stiffness k = 3750 kN/m
Damping c = 50 kNs/m
Natural frequency of vibration \omega =\sqrt{\frac{k}{m} } = 9.6825 rad/s
Period of vibration T = 2π/ω = 0.6489 sec
Critical damping c_{c} = 774.5967
Damping ratio x = c/c_{c} = 6.45%
The inertia force m\ddot{x}(t), damping force c\dot{x}(t) and spring force kx(t) are shown in Figure 2.10. The sum of these forces at any instant t is zero. It can be seen that in the present case the damping force is quite small as compared to the other two forces.
