Damped and Driven Oscillation of a Bridge

In summary: I then found the force (k=F/m) and substituted it into the equation for amplitude. I then solved for T and found that it was 6T.
  • #1
Canuck156
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0
Sorry that I had to use an image file, I was having a lot of trouble using the Latex system.

http://www.flamingice.5gigs.com/Question.gif

Ok... We know the amplitude of the oscillations, and the force per person, so all we need to do is find Fmax, by finding other values and substituting into the equation for amplitude.

By using the equation for oscillation of an underdamped system I have found that b=m/3T, where T is the period of the undriven, undamped system, but I'm not sure how to find T in order to get a numerical value for b. I could find it if I knew k, the force constant of the system, but I have no idea how to find that.

So, I guess that my question is, how do I find the k of the system? If I know that, I think I'll be able to solve the rest of the problem.

Thanks!
 
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  • #2
Well, your quote says: "Take the damping constant to be such that the amplitude of the undriven oscillations would decay to 1/e of its original value in a time t= 6T where T is the period of the undriven, undamped system."

The "undriven, undamped" system has equation of the form my"+[itex]\omega_n[/itex] = 0 and so has solution of the form y= A cos([itex]\omega[/itex])+ B sin([itex]\omega[/itex]). What is [itex]\omega[/itex] for that system? What is its period, T? What it 6T? What must k be so that the solution to my"- ky'+ [itex]\omega_n[/itex]y= 0 reduces to 1/e of its original value in time 6T?
 
  • #3
I can see what you mean (I think :smile: ). If I knew [itex]\omega_n[/itex] I would be able to solve the problem. However, I'm not sure how I should go about finding [itex]\omega_n[/itex]. In the physics course that I'm taking we are not really expected to be able to solve differential equations.

Thanks!
 
  • #4
Anybody got any ideas?
 
  • #5
I've solved it now... I was supposed to assume that since resonance was occurring, the natural frequency was approximately equal to the frequency of the driving force.
 

1. What is a damped and driven oscillation of a bridge?

A damped and driven oscillation of a bridge refers to the movement of a bridge caused by external forces (driving) and internal forces (damping). These forces can cause the bridge to vibrate or sway, and can impact the stability and safety of the structure.

2. What factors affect the damped and driven oscillation of a bridge?

The damped and driven oscillation of a bridge can be affected by various factors, including the design and construction of the bridge, the materials used, the wind and weather conditions, and the presence of any external forces such as traffic or earthquakes.

3. How does damping impact the oscillation of a bridge?

Damping is the mechanism by which energy is dissipated from a vibrating system, such as a bridge. In the case of a damped and driven oscillation of a bridge, damping can help to reduce the amplitude of the vibrations and provide stability to the structure.

4. What are some methods used to dampen the oscillation of a bridge?

There are several methods used to dampen the oscillation of a bridge, including the use of dampers (such as shock absorbers) at strategic points on the bridge, changing the materials or design of the bridge to reduce vibrations, and implementing regular maintenance and monitoring of the structure.

5. Can the damped and driven oscillation of a bridge be predicted?

While it is not possible to predict the exact behavior of a bridge during a damped and driven oscillation, engineers and scientists can use mathematical models and simulations to estimate the potential effects of external forces and identify potential areas of concern. Regular monitoring and maintenance can also help to prevent or mitigate any potential issues.

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