Question

A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor (ratio) is 0.25, the amplitude of steady state oscillation at resonance is ______ mm.

Answer 1

Concept:

Steady state Amplitude:

\(A = \frac{{{f_0}/k}}{{\sqrt {{{\left( {1 - {{\left( {\frac{\omega }{{{\omega _n}}}} \right)}^2}} \right)}^2} + {{\left( {2\varepsilon \frac{\omega }{{{\omega _n}}}} \right)}^2}} }}\)

At resonance ω = ω_n i.e. damped frequency is equal to natural frequency

\(A = \frac{{{f_0}/k}}{{2\varepsilon }}\)

Calculation:

\({\left( {Amplitude} \right)_{Resonance}} = \frac{{{F_0}}}{{2\varepsilon k}} = \frac{{100}}{{2 \times 0.25 \times 10 \times 1000}}\)

x = 0.02 m = 20 mm