Derive the equation of motion given in Eq. (1) of Example 9.6 for the system in that examp...

Derive the equation of motion given in Eq. (1) of Example 9.6 for the system in that example. The independent variable y is measured from the equilibrium position of the system, m is the mass of the motor and platform, c is the total damping coefficient of the dashpots, k is the total constant of the linear elastic springs, ωr is the angular velocity of the unbalanced rotor, ε is the distance of the eccentric mass from the rotor axis, and mu is the eccentric mass. Note that m includes the eccentric mass so that the nonrotating mass is equal to m − mu.

Figure P9.54