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 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 = 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 meters above the equilibrium position.