Suppose that m = 75 slugs (the car weighs 2400 lb), L₁ = 7 ft, L₂ = 3 ft (it's a rear-engine car), k₁ = k₂ = 2000 lb/ft, and I = 1000 ft-lb-s². Then the equations in (40) take the form

(a) Find the two natural frequencies ω₁ and ω₂ of the car.
(b) Now suppose that the car is driven at a speed of v feet per second along a washboard surface shaped like a sine curve with a wavelength of 40 ft. The result is a periodic force on the car with frequency ω = 2πv/40 = πv/20. Resonance occurs when ω = ω₁ or ω = ω₂. Find the corresponding two critical speeds of the car (in feet per second and in miles per hour).

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75x" + 4000x - 80000 = 0, 8000x + 116,0000 = 0. 10000"