Problem $4(20)$

A sensitive instrument that is required to be insulated from vibration is to be installed in a laboratory. The vibrations of the floor of the laboratory may be assumed to be a simple harmonic motion having a frequency in the range $1,000$ to $3,000$ cycles per minute. The instrument is to be mounted on a small platform and supported on four springs arranged to carry equal loads. The combined mass of the instrument and supporting table is $150$ lb $.$ Calculate a suitable value for the stiffness of each spring if the amplitude of transmitted vibrations is to be less than $10\%$ of the floor vibrations over the given frequency range. Assume that the damping is negligible. Now, if the springs are to be replaced by four rubber isolators which provided only one half of the spring stiffness but will introduce damping to the system. Find out what will be the damping coefficient to maintain the same effectiveness of the isolation system. Could adding the extra mass to the system be an effective way to design the isolation system?