Suppose that a car oscillates vertically as if it were a mass ofm = 800 kg on a single spring with spring constant k = 7 × 104 N/mwhich is attached to a single damper with c = 3000 N·s/m. Supposethat this car is driven along a sinusoidal road surface with anamplitude of 5 cm and a wavelength of L = 10 m.
1.Write the non-homogeneous ODEthat governs the vertical motion of the car. (Make sure to keeptrack of units).
2. Find the steady-stateamplitude of vibration of the car as a function of the horizontaldriving speed v (m/s).
3. At what driving speed vm willthe greatest amplitude of vertical vibrations occur?
4. If the driver would preferthat the car oscillates with a lower amplitude than that of theunderlying road surface (i.e. A < 5 cm), in what range of speedsmust they drive?
