# Physics Simulation of a Simple Pendulum with Drag Forces

I am working on simulating a simple pendulum with present drag forces. My task is to use numerical methods (I am using Verlet integrator) to estimate the angle as a function of time, as well as the angular velocity and acceleration.

I am supposed to track the motion of the pendulum for 24s to measure the angle and angular velocity evolution and make a phase space diagram of these.

Even for a dt of 0.001, at 0.1 seconds I observe this:

It is worth noting that at the end of the simulation for this case, the steps taken are about 100,000.

I know that error-build up must be an issue here.

My question is, do I have to find another numerical method to estimate this oscillation that can handle this task? Or am I not using Verlet correctly?

• The frequency of your simple pendulum seems to be about 300 Hz. That corresponds to a pendulum less than 3 microns long. It is tricky to build a pendulum this small. Perhaps there is some problem with your code. – Ben51 Oct 11 '19 at 3:23
• Your oscillation amplitude is increasing with time. Is this what you expect? Probably you should double-check your calculation. – Gilbert Oct 11 '19 at 11:45
• What are the dynamics equations you are using? And which Verlet implementation? – Kyle Kanos Oct 11 '19 at 12:09
• For quadratic drag (i.e., $F_\text{drag}\propto v^2$), you can't use straight Verlet methods, it has to be modified. See this post of mine – Kyle Kanos Oct 11 '19 at 12:15
• 1. Your drag term seems to have the wrong sign. 2. Your problem seems to be at 180 degrees, i.e. vertical. 2'. Plot including 0 and using multiples of 30 or 45 degrees. 3. Show on the same plot what happens without drag, just to check. – Mathieu Bouville Oct 12 '19 at 8:25