A single-degree freedom spring-mass system is subjected to a sinusoidal force of 10 N amplitude and frequency ω along the axis of the spring. The stiffness of the spring is 150 N/m, damping factor is 0.2 and the undamped natural frequency is10ω At steady state, the amplitude of vibration (in m) is approximately
0.07
The frequency ratio is r = ω/ωn = 0.1. Thus \(X=\frac{10/150}{\sqrt{(1-0.1^2)^2+(2\times0.2\times0.1)^2}}=0.0673\ \mathrm m\approx0.07\ \mathrm m\).
Important Questions from Transmissibility and Magnification Factor
When ω/ωn = 1, the transmissibility is
where ω = frequency of excitation, rad/s
ωn = Natural frequency, rad/s
The Transmissibility of a vibrating system, for the values of (ω/ωn) >√2, will be
A vibrating system having a mass of 30 kg is supported by 4 springs, each having a stiffness of k. The system runs at 420 rpm. If only 10% of the shaking force is allowed to be transmitted to the supporting structure, then the value of stiffness k will be close to:
For a single degree of freedom viscous damped system, if the frequency ratio is greater than √2, it implies that:
Dynamic Magnification Factor is computed as:
