2. Suppose that you are designing a new shock absorber for an automobile. The car has a mass of 500 kg (kilograms) and the combined effect of the springs in the suspension system is that of a spring constant of 4000 N/m (i.e.each of the four springs has a spring constant of 1000 N/m). 1. Before a damping mechanism is installed in the car, when the car hits a bump it will bounce up and down. How may bounces will a rider experience in the minute right after the car hits a bump? Alternatively, what is the frequency in cycles per minute? The car will bounce 27 times per minute. 2. Your job is to design a damping mechanism which eliminates oscillations when the car hits a bump. What is the minimum value of the effective damping constant that can be used? y= 2828.8 kg/sec. 3. Suppose that at time t=0 the car hits a bump. Immediately before that time the car was not moving up and down and the effect of the bump is to add a vertical component to the speed of the car of 1.0 meter/sec. How high will the car rise above its equilibrium position if you design the system with the damping constant you found in part (b)? It will rise 0.555 X meters above the equilibrium position.