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

In summary, the student is trying to solve a differential equation to determine the net forces on two attached rods. They are looking for someone to help them, but if they cannot find anyone, they will just have to figure it out on their own.
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!

#### Attachments

• Untitled-1 copy1.jpg
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So there's no one to help me :(

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.

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## 1. What is dynamic systems physics?

Dynamic systems physics is a branch of physics that studies the behavior and interactions of complex systems over time. It involves the use of mathematical models and computer simulations to understand the dynamics of these systems.

## 2. How is dynamic systems physics different from classical physics?

Classical physics focuses on studying the behavior of isolated objects, while dynamic systems physics looks at the behavior of interconnected systems. Dynamic systems physics also takes into account the effects of time and feedback loops, which are not typically considered in classical physics.

## 3. What are some real-world applications of dynamic systems physics?

Dynamic systems physics has a wide range of applications, including weather forecasting, traffic flow analysis, stock market prediction, ecological modeling, and understanding the spread of diseases. It is also used in engineering to design and optimize complex systems such as aircrafts and bridges.

## 4. What are some important concepts in dynamic systems physics?

Some important concepts in dynamic systems physics include chaos theory, bifurcation theory, and self-organization. Chaos theory studies the behavior of systems that are highly sensitive to initial conditions, while bifurcation theory examines the changes in a system's behavior as parameters are varied. Self-organization refers to the emergence of complex patterns and structures in a system without external control.

There are many resources available for learning about dynamic systems physics, including textbooks, online courses, and research papers. It is also helpful to have a strong foundation in mathematics and physics principles. You can also attend conferences and workshops to stay updated on the latest developments in the field.

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