A tractor chassis excites a seat at 20 rad/s. Damping is 400 N·s/m, critical damping1600 N·s/m, and seat-plus-operator mass80 kg. Find vibration transmissibility, to two decimals.
Damping ratio is $\zeta=c/c_c=400/1600=.25$. Since $c_c=2m\omega_n$,natural frequency is $\omega_n=1600/(2\cdot80)=10$ rad/s; frequency ratio r=2. For base excitation, $$TR=\sqrt{\frac{1+(2\zeta r)^2}{(1-r^2)^2+(2\zeta r)^2}}=\sqrt{2/10}=.4472136.$$ Thus **.45**.
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