### Calculate the amplitude of vertical motion of the machine

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A machine is supported on four steel springs for which damping can be neglected. The natural frequency of vertical vibration of the machine-spring system is 200 cycles per minute. The machine generates a vertical force p(t)=p0sinwt. The amplitude of the resulting steady-state vertical displacement of the machine is u0=0.2 in. when the machine is running at 20 rpm, 1.042 in at 180 rpm, and 0.0248 at 600 rpm. Calculate the amplitude of vertical motion of the machine if the steel springs are replaced by four rubber isolators which provide the same stiffness, but introduce damping equivalent to 25% for the system. Comment on the effectiveness of the isolators at various machine speeds

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