Suppose that a car oscillates vertically as if it were a mass of m = 800...

Suppose that a car oscillates vertically as if it were a mass of m = 800 kg on a single spring with spring constant k = 7 × 104 N/m which is attached to a single damper with c = 3000 N·s/m. Suppose that this car is driven along a sinusoidal road surface with an amplitude of 5 cm and a wavelength of L = 10 m.

1.Write the non-homogeneous ODE that governs the vertical motion of the car. (Make sure to keep track of units).

2. Find the steady-state amplitude of vibration of the car as a function of the horizontal driving speed v (m/s).

3. At what driving speed vm will the greatest amplitude of vertical vibrations occur?

4. If the driver would prefer that the car oscillates with a lower amplitude than that of the underlying road surface (i.e. A < 5 cm), in what range of speeds must they drive?

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genius_generous answered 1 year ago

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