The problem is modelling a bridge wobbling from side to side. x is the displacement from its normal position. Ax''+Bx'+Cx=0 and A, B and C are all defined as numbers.

The question is show that the level of damping here is only 1% of the critical value. What does critical value mean? I know what critical damping is, but that is only when the discriminant=0.

Question

The problem is modelling a bridge wobbling from side to side. x is the displacement from its normal position. Ax''+Bx'+Cx=0 and A, B and C are all defined as numbers.

The question is show that the level of damping here is only 1% of the critical value. What does critical value mean? I know what critical damping is, but that is only when the discriminant=0.

henryblah · Answer

If it helps, the question also says at a critical number of pedestrians (160) the bridge starts wobbling.

unklerhaukus · Answer

What numbers are A,B,C ?

amistre64 · Answer

it an homogenous diffy Q with constant coefficients ....

amistre64 · Answer

i got no idea at the moment what the critical value stuff is taking about :/

amistre64 · Answer

maybe we find the solution to x, and take its derivative?  or do we take the derivative of the equation that is presented after knowing what x could be?

henryblah · Answer

I've asked a few of my friends and have worked out the answer. If it is any use to you guys. Apparently the 'B' Is the thing you can change the damping with. So all you have to do is work out what B needs to be for critical damping and work out the ratio. which happens to be close to 1%. But thanks anway guys.