Problem

Problems deal further with the car of Example. Its upward displacement function satisfies...

Problems deal further with the car of Example. Its upward displacement function satisfies the equation mx″ + cx? + kx = cy′ + ky when the shock absorber is connected (so that c > 0) With y = a sin ωt for the road surface, this differential equation becomesmx″ + cx′ +kx = E0 cosωt + F0 sin ωtwhere E0 = cωa and F0 = ka.

Apply the result of Problem to show that the amplitude C of the resulting steady periodic oscillation for the car is given by

Because ω = 2πυ/L when the car is moving with velocity υ, this gives C as a function of υ.

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Solutions For Problems in Chapter 2.6

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