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

[Omkar Vaidya]

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

 

[Ray Vickson]

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.

 

[Omkar Vaidya]

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.

 

[Ray Vickson]

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.

 

[Omkar Vaidya]

Your post speaks of a "site", but does not give a link.

https://services.math.duke.edu/education/ccp/materials/diffeq/pendulum/pend1.html
https://en.wikipedia.org/wiki/Damping_ratio