How to model a non-linear pendulum with air resistance?

AI Thread Summary
The discussion revolves around modeling a non-linear pendulum with air resistance, focusing on the differential equation that incorporates a resistive force. It highlights the need for a force that changes direction, suggesting the use of k v^2 sign(v) to accurately represent damping. The main inquiry is how varying the area (A) affects damping, with references to external resources for analysis. Participants emphasize the importance of using a reliable numerical differential equation solver for accurate results. The conversation underscores the complexities of modeling damping in pendulum motion.
Omkar Vaidya
Messages
10
Reaction score
0

Homework Statement


I have found a differential equation that models a non-linear pendulum with air resistance, and now I have data. I've looked at the following site for guidance on how to analyse the data. It compares the motion of a damped spring, and compares it to the motion of a damped pendulum. However, my equation involves a v^2 (or (dtheta/dt)^2. The equation in the site has v proportional to the drag force. The question I am trying to answer is "How does changing the value of A(area) affect damping?"

Homework Equations



https://prnt.sc/i6bfv0[/B]

The Attempt at a Solution

 
Last edited:
Physics news on Phys.org
Omkar Vaidya said:

Homework Statement


I have found a differential equation that models a non-linear pendulum with air resistance, and now I have data. I've looked at the following site for guidance on how to analyse the data. It compares the motion of a damped spring, and compares it to the motion of a damped pendulum. However, my equation involves a v^2 (or (dtheta/dt)^2. How would I eliminate this problem?

Homework Equations



https://prnt.sc/i6bfv0[/B]

The Attempt at a Solution


As already pointed out in another thread on this problem, your differential equation is incorrect. You cannot have a resistive force of ##k v^2##, because that always points one way (always either to the left or to the right). You need a force that changes direction when the pendulum reverses its motion. That can be done using ##k v^2\: \text{sign}(v) = k v |v|##.

I don't think you can "eliminate" the problem; you can only deal with it. If you have access to a good numerical DE solver, getting a reliable numerical solution should not be much of a problem. In another thread on this problem I presented solutions obtained by Maple.
 
Last edited:
Ray Vickson said:
As already pointed out in another thread on this problem, your differential equation is incorrect. You cannot have a resistive force of ##k v^2##, because that always points one way (always either to the left or to the right). You need a force that changes direction when the pendulum reverses its motion. That can be done using ##k v^2\: \text{sign}(v) = k v |v|##.

I don't think you can "eliminate" the problem; you can only deal with it. If you have access to a good numerical DE solver, getting a reliable numerical solution should not be much of a problem. In another thread on this problem I presented solutions obtained by Maple.

Yes, I think that would be my question too. I did change the v^2. However, the question I am trying to answer (sorry for not including that) is "How does changing A(area) affect damping?" That is where the site comes into use, by comparing damping coefficients.
 
Omkar Vaidya said:
Yes, I think that would be my question too. I did change the v^2. However, the question I am trying to answer (sorry for not including that) is "How does changing A(area) affect damping?" That is where the site comes into use, by comparing damping coefficients.

Your post speaks of a "site", but does not give a link.
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'Collision of a bullet on a rod-string system: query'
In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top