How can I solve a problem involving dynamic systems in physics?

[adysa]

I have really big prob., please. anyone who know how to do this i'll be very pleased.


My Homewok is little problem.We work Dynamic systems and then we test that system on computer ( on Mathlab).I attached you my prob. you and I'll translete you upper text:

Two equal bars AiBi length Li=L, mass mi=M, can spin around crank Oi, i=1,2... On ends of bars are connected my mass mi=m=M/6.bars are connected with spings rigidity ki=k.

Well I have to write diferential equl. form of this system.(do it by energys-potencial & kinetical).

you have my prob. on attachment!
if anyone has solution of this prob. please email me: adipoljak@gmail.com

 

[adysa]

So there's no one to help me :(

 

[arildno]

I won't bother with the horizontal displacements' effects on the spring forces, those effects should be tiny anyway.
Let's look at A2 first:
If A2 is displaced a vertical distance Y, then the spring at the ground (situated L/3 from the attachment on the wall, and 2L/3 from A2) will stretch a distance Y/3, generating a downward force -kY/3.
The attachment point with the middle spring will raise to a level Y/2 above the horizontal level.

Now, let us consider A1:
If this goes up a distance y, then the spring midpoint to O1 is comressed y/2, yielding a downwards force -ky/2.
At the same time, B1 will sink to a position y/3 less than the horizontal level.

Thus, the middle spring will experience a net compression Y/2+y/3 as a result of both rods moving, yielding a compressive force -k(Y/2+y/3) on the lower rod, and k(Y/2+y/3) on the upper one.

See if you agree so far with me.

In order to continue on your own, here's a programme you need to get through:
1. In order to eliminate the reaction forces at the wall and O1, it is most convenient to compute the net torques about these, using the moment-of-momentum equations.

2. Thus, you'll gain differential equations in angular displacements, so you'll need to calculate the correct moments of inertia, along with the relationships between vertical displacements and angular displacements.

3. Now, you should have a non-linear system of two equations and two unkowns, this can be entered into some computer solving routine.
Alternatively, you may linearize your equations, and derive approximate solutions for tiny angular displacements by hand calculation.