A wheel-and-tire assembly is being tested on a tire balancer. The wheel-and-tire assembly is slightly out of balance. If this wheel were on a car, the car could be very difficult to control.

What is known:

slider mass m_{1} = 20 kg

wheel and tire mass m_{2} = 25 kg

spring constant k = 7,000 N/m

damping constant c = 56 N s/m

eccentricity d = 1 cm

rotation speeds 90, 120, 150 rpm

Question

What is the equation of motion for the platform on which the wheel is mounted?

Approach

Determine the differential equation of motion.

Solve the differential equation for the homogeneous and particular parts.

Apply the initial conditions to the complete solution of the differential equation.

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