A vehicle of mass m 900 kg travels over a long terrain that is approximately sinusoidal: 2TS y= dsin where 1.6 m and d = 10 mm. The suspension stiffness k = 8 x 104 N/m and the system has a damping ratio of 0.2 x 1.6 m d 10 mm (a) Determine the amplitude of the steady-state vibration of the vehicle if it travels at speed v = 40 m/s (b) Determine the speed of the vehicle for which the vehicle has the maximum amplitude.

The motion y(t) is the input to the system and the motion of the body x(t) is the output of the system. A motorcycle is travelling at a speed of 55 mph on a road with a sinusoidal elevation. The distance between peak-to-trough is 3 ft and the distance between two consecutive peaks is 50 ft. The natural frequency of the suspension system is 5 rad/sec and the damping ratio is 0.2. Determine the amplitude of vibration in x.

[6] An instrument panel weighing 30 lb is installed in a vehicle on a flexible mount that has an equivalent stiffness k = 400 lb/in and negligible damping. As a result of engine vibration, the vehicle vibrates with a steady-state amplitude of o.25 in at a frequency of 40 Hz. Determine the steady-state amplitude of vibration of the instrument panel.

Answer ASAP would be appreciated