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This is a forced, steady state vibration situation.
There are 2 supporting springs, hence net stiffness Ke=2k
Damping coefficient Ce = 0.05 Cc = 0.05*2*sqrt(Ke*m)
The expression for desired amplitude Y is
Y=Fo/sqrt((ke-m*w^2)^2+(Ce*w)^2)
Y will be maximum at resonance, i.e., w=wn
Thus the design condition is k=(1/2)m*w^2
k=21.73 kN/m
At resonance, Y=Fo/c*w
The peak solenoid force required is 2.17 N
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