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In absence of damping,
TR=1/(1- r^2)
where r=w/wn
Natural frequency wn=20.57 rad/s
(a) Combined stiffness=42.30 N/mm
(b) In actual conditions, successive vibrations are reduced by 30%
Logarithmic decrement delta=ln(X/Xn+1)
X/Xn+1 = 1/1-0.3
delta= ln(X/Xn+1)= (2*pi*zeta)/sqrt(1-zeta^2),
where zeta=damping factor
zeta=0.05668
Transmissibility ratio is given by
TR=sqrt(1 + (2*zeta*r)^2)/sqrt((1- r^2)^2 + (2*zeta*r)^2)
TR=0.05632
The Maximum unbalance force is Fo=999.30 N
Force transmitted is Ftr=Fo*TR =56.28 N
(c) At resonance, r=1
TR=sqrt(1 + (2*zeta)^2)/(2*zeta)
TR=8.879
Maximum unbalanced force due to resonance Fo=47.59 N
Force transmitted at resonance Ftr=422.50 N
(d)Amplitude at resonance X=Ftr/Ke =9.989 mm
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