Particle Dynamics Project Fall $24$

WHAT MORE INFORMATION DO YOU WANT??? THERE IS NOTHING ELSE$$ DONT WORRY ABOUT THE PHYSICAL MODEL

THERE IS NO OTHER INFORMATION THIS IS IT

This is all the information given, In just need the matlab code to solve

This is a group assignment that is part of your Projects score.

The $3-$kg block $\backslash ($ A $\backslash )$ is free to move on the horizontal surface. The $\backslash (2-\backslash$mathrm$\{$kg$\}\backslash )$ block $\backslash ($ B $\backslash )$ is attached to $\backslash ($ A $\backslash )$ and swings freely on a rope of length $0\mathrm{.}2$ m $.$ The system is released from rest at $\backslash (\backslash$theta$=30^\{\backslash$circ$\}\backslash ).$

$1)$ Determine $($and display$)$ the EOM$($s$)$ for the system.

$2)$ Integrate the EOM$($s$)$ for $5$ seconds using ode$45.$ Plot the resulting displacements vs time.

$3)$ Create an animation showing the motion of the system in Cartesian Coordinates. Use "axis equal" to make the $\backslash ($ x $\backslash )$ and $\backslash ($ y $\backslash )$ increments the same.

$4)$ Linearize the EOMs. Solve these linearized EOMs analytically $-$ do not use ode$45.$ Create plots comparing the nonlinear and linearized displacements vs time. Discuss whether or not the linearized solution represents the nonlinear solution well.

$5)$ Include the following checks in Step $9.$

Units:

$-$ Confirm units. You can do this analytically $($by hand$)$ or using MATLAB's symunit command. Check units for each of the fundamental equations, the resulting nonlinear EOMs, and the forces. Be sure to show the actual units for each quantity.

Magnitude:

$-$ Plot the normal and tension forces vs time. Discuss whether the values are reasonable.

$-$ Plot the kinetic, potential and total energy vs time. Use the attachment point at block $\backslash ($ A $\backslash )$ as your datum for potential energy. Also plot the change in energy $($as a percentage$)$ vs time. Discuss whether the results are reasonable.

$-$ Discuss any other checks on magnitude that you believe help validate your results.

Signs:

$-$ Confirm that the signs on various quantities make sense.

Do all your work in a MATLAB LiveScript using the Symbolic Toolbox. Follow the $9-$Step Process, including thorough checks of your solution, and document your work. Note that $\backslash (10\backslash \%\backslash )$ of your grade will be based on the quality of the write$-$up of your results. Include your team number and team member names in your report. Include all hand$-$calculations in an Appendix or the body of your report. Submit your report as a PDF file.

EXTRA CREDIT $($up to $4$ pts$)$:

Build and test a physical model of the system $-$ your choice of materials. Since your system parameters will probably be different than above, re$-$run your MATLAB code using your parameters. Calculate and compare the measured and calculated frequencies of oscillation. Upload your results and a video of your system in operation to Canvas. write the matlab code