Question

1. Suppose that a car weighing 4000 pounds is supported by four shock absorbers Each shock absorber has a spring constant of 6500 lbs/foot, so the effective spring constant for the system of 4 shock absorbers is 26000 lbs/foot.

1. 1. Assume no damping and determine the period of oscillation of the vertical motion of the car. Hint: g= 32 ft/sec2

2. 2. After 10 seconds the car body is 1 foot above its equilibrium position and at the high point in its cycle. What were the initial conditions?

3. 3. Now assume that oil is added to each the four shock absorbers so that, together, they produce an effective damping force of -6.93 tb-sec/ft times the vertical velocity of the car body. Find the displacement y(t) from equilibrium if y(0)=0 f and y(0)=-10 ft/sec.

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 2000 ~N m (L.e.eech of the four springs has a spring constant of 500 ~N m).

1. 1. Before a damping mechanism is installed in the cat, 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? Afematively, what is the frequency in cycles per minute?

   
   

2. 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?

   
   

3. 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 burp is to add a vertical component to the speed of the car of 1.0 metric. How high will the car rise above its equilibrium position if you design the system with the damping constant you found in part (b)?

Answer 1

Forst i solved 2nd one it was correct

then i tried doing 1st one

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