Recent content by HansBu

It is quite consistent with the mechanics of Kapitza's pendulum. I presume that something is wrong in the problem, right?

Hi, mitochan! There were no specified conditions for ##T_d## given in the problem.

I understand that when $$A_0 \gg g$$, the g term in the equation of motion can be dropped. The equation of motion then becomes $$\frac{d^2\theta}{dt^2}=-\frac{a_d(t)}{L}\sin\theta$$ But how can I show that the pendulum is stable for such case? I am totally clueless.

Have you seen the figure? The plane is parallel to the xz-plane not on the xy-plane. I think you missed it and I cannot see the logic as to why we should consider x and y only instead of x and z

I am a bs physics 2 student and only knowledgeable on Laplace's Equation on Cartesian Coordinate System for electrostatic problems. Usually, the method is restricted only on variable separation and my only main problem here is the boundary condition. I am sorry for the trouble.

Clearly, the potential has no dependence on y. Hence, I am to arrive at a potential function in term of x and z only. Am I right?

From the problem, I can deduce the following boundary conditions: 1. As x approaches infinity, V = Vo 2. As x approaches negative infinity, V = -Vo

What I am having trouble here is looking for the set of boundary conditions.

I really have no idea as to how to attack the problem in the first place. I am here to ask for some generous help on how to start. The figure is shown below for reference.

Here is the Chen System I am given the initial condition (t=0) that a particle lies on the xyz-plane at a point (-10,0,35). I was notified that if I plugged in a=40, b=5, and c=30, the trajectory of the particle will be chaotic. On the other hand, if I retained the values of a and c, and...

Hello, Wrobel! Can you enlighten me more on what you are trying to imply?

Yes sir, I did only to see the standard differential equation of a damped driven pendulum in normalized version. Now, I am really confused. The graph above, from the problem, says that those are chaotic solutions. I understand what the problem means, but chaotic solutions of what system?

Here are the nonlinear and coupling ordinary differential equations: I was given values of a, b, and c as well as some initial values for x, y, and z. If ever the equations above are related to the pendulum, I can think of a as the damping factor, b as the forcing amplitude, and c as the...

Yes. That is what I meant. Is the math wrong?

It doesn't have a negative sign on it. The one about z_o = 1, I think it's wrong because I validated it using WolframAlpha.