Problem Diagram

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 m₁ = 20 kg
• wheel and tire mass m₂ = 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

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

• 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.