Calculating Spring and Damping Constants for a Car Suspension System

  • Thread starter ChazyChazLive
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In summary, the spring and shock absorber system of one wheel supports 550 kg and the oscillation damping rate is BY 55% every cycle.
  • #1
ChazyChazLive
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Homework Statement


The suspension system of a 2200 kg automobile "sags" 14 cm when the chassis is placed on it. Also, the oscillation amplitude decreases by 55% each cycle. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming each wheel supports 550 kg.

Homework Equations


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The Attempt at a Solution


I found k by making mg=-kx
k=38500 N/m
part B i found it to be 876 kg/s.
However, this answer is wrong.
I'm not sure what's wrong here but the formula I used works with everyone elses example.
e ^ (-bt / 2m) = 55/100
I found T to be 0.751 using T=2pi radical (m/k)
 
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  • #2
What did you use for t when solving for b?
 
  • #3
The oscillation damping rate is BY 55% every cycle, hence we have:

[tex]x(t+T)=x(t)-0.55\cdot x(t)=0.45\cdot x(t)[/tex]
 
  • #4
To NBAJam100: I used the T I found
To Thaakisfox: I don't really understand what you wrote. It looks confusing. Not sure how to apply it.
 
  • #5
Well you want to find the ratio of the amplitudes between cycles.
At time t let the position be x(t). Let the period of oscillation be T. Then the position after one cycle will be: x(t+T).

But we know the x(t) function, so:

[tex]\frac{x(t+T)}{x(t)}=e^{-bT/2m}[/tex]

But it is also given that the amplitude decreases BY 55% every cycle, so:

[tex]x(t+T)=x(t)-0.55x(t)=0.45x(t) \Longrightarrow \frac{x(t+T)}{x(t)}=0.45[/tex]

Combining these you will get the result...
 
  • #6
Oh, I see. That makes a lot of sense. Then I just plug it in and I got 1170kg/s. My confusion with the capital and lower t's got me mixed up. Thankyou very much. =]
 

FAQ: Calculating Spring and Damping Constants for a Car Suspension System

What is an oscillation problem with damping?

An oscillation problem with damping involves a system that is experiencing periodic motion, but also has a force acting against the motion, causing it to eventually come to a stop.

What factors affect the damping in an oscillation problem?

The amount of damping in an oscillation problem can be affected by factors such as the amplitude of the oscillation, the mass of the system, and the strength of the damping force.

How is damping calculated in an oscillation problem?

Damping can be calculated in an oscillation problem using the damping ratio, which is the ratio of the actual amount of damping to the critical damping value for the system.

What is critical damping in an oscillation problem?

Critical damping is the ideal amount of damping needed to prevent oscillations from occurring in a system. It is the point at which the system will return to its equilibrium position in the shortest amount of time without oscillating.

How can damping be increased or decreased in an oscillation problem?

Damping can be increased by increasing the strength of the damping force or by increasing the mass of the system. It can be decreased by decreasing the strength of the damping force or by decreasing the mass of the system.

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