Data Analysis

Deliverable 17: For each of your eight experiments, create a simulation of an identical pendulum with identical initial conditions. For each experiment, plot the angle versus time for both the experimental data and the simulated data. This should result in four plots for the single pendulum experiments and eight plots of the double pendulum experiments (two angles per experiment). Make sure each of your 12 plots are clearly labelled. 

Deliverable 18: For each of the 12 plots in deliverable 17, computing an error metric (MSE, RMSE, percent error, etc.) to determine how closely the experimental results match the simulations. 

Deliverable 19: Using numerical differentiation techniques (either that you wrote or that you import from a code library) compute the second derivative of the angles with respect to time (you should have a total of 12 sets of derivatives). Compare these derivatives with their expected values from the Theoretical Modelling section. Report your results using graphs and/or error metrics.

Deliverable 20: Using your single pendulum experiment at a small angle, compare it to a simple pendulum. Do the same for a single pendulum experiment at a large angle. Is the simple pendulum model better (or equivalent) to the single pendulum model at either of these initial conditions?

Deliverable 21: Answer the following questions:

• Which experiments matched the simulation most closely? Why do you think they match for these experiments? 

• Which experiments did not match the simulations and why?

• Do the angular accelerations of the experiments match the simulations? What may be causing differences?

• How could you build a better single pendulum or double pendulum that would more closely match your simulations?