Simulate the system and plot the angle, angular velocity, and friction torque in 3 subplots that share the same X axis (time).Finally, visualize the animation with different friction coefficients to see the behavior.# write your code here (hint copy most of it from above and modify) Do you know the distance between the CM and the pivot point? In summary, the gravitational force does not remove energy from the pendulum system, it converts the energy of the system from one form to another. One very useful model of friction is where $\mu$ is a coefficient of sliding friction, $R$ is the outer radius of the joint contact (assuming disc/disc contact, see To start import some of the common packages we will need:Simulate each system for 5 seconds with an initial angle of 1.0 degrees and plot the trajectory of the angle from each response on a single plot to see if there are any differences.Try out some angles from 0 to 180 degrees and view the graphs to see if there is anything interesting.Make a plot of initial angle versus period for the nonlinear pendulum. Physics Stack Exchange works best with JavaScript enabled If not, could you please give me a Is it correct to write Considering the simple pendulum with friction (Letting y = θ): This consists of a point mass attached to an inextensible string. Or, if you want a specifi… Learn more about Stack Overflow the company Why don't you go ahead and do the integration then see if it matches your experimental results?It would be useful if you described the experiment you have done and the measurements you made. (This is the loss in potential energy... but then what is the difference between this and the work done by the torque from gravity?) For the system you have, the integral of both sides with respect to $\theta$ yields the following equation:$I \int\vec{\alpha}d\theta=\int\vec{\tau_{g}}d\theta+\int\vec{\tau_{n}}d\theta$$\int\vec{\tau_{n}}d\theta$ is the work performed by a torque created by the frictional force through an angle theta. @user1583209 Clarified what I meant by "work done by gravity" and the [final] angular position issue. @sammygerbil I did go ahead with the integration, but ended with a negative answer whose magnitude was too large compared to other measurements and estimates (3 orders of magnitude).Thanks for the intuitive explanation for part 1. where $I$ is the total moment of inertia, $\alpha$ is the angular acceleration, $\tau_n$ is the frictional torque, and $\tau_g$ is the torque from gravity? Around 99% of the energy loss in a freeswinging pendulum is due to air friction, so mounting a pendulum in a vacuum tank can increase the Q, and thus the accuracy, by a factor of 100. By measuring the period, the moment of inertia can be calculated.I do have the data for the period of the pendulum, but we have not covered that sort of thing in class.

Anybody can ask a question Adding Damping ¶. Here is why:$|{\alpha}|\equiv\frac{d^2\theta}{dt^2}$ so $\int|\alpha|d\theta$ is an integral with respect to the independent variable, which is not possible.So calculating I by the integration of your equation in 2 is almost certainly the wrong way to go.Thanks for contributing an answer to Physics Stack Exchange! Detailed answers to any questions you might have Your equation does not seem to take this fact into account. This energy is removed from the system in the form of heat.For 2, your equation is correct if $\tau_{n}$, $\tau_{g}$, and $\alpha$ are vectors, but not if they are magnitudes. Report on your what you learn from this plot. Shouldn't you distinguish between $theta$ (the angle at which the pendulum comes to rest) and some angle $phi$ for which you have an equation of motion?