apparent until a solution over time is attempted. Your project involves such a case.

A mass m is constrained to the surface of a disk of radius R by a

spring with spring constant k and unstretched length $($R$)/(2).$ The disk

lies in the horizontal plane $($no gravity$).$ The mass is attached to

the disk in a shallow groove so that it cannot leave the surface.

Constants for the problem are m$=0\mathrm{.}2$kg$,$R$=0\mathrm{.}25$m$,$k$=1000$

$($N$)/($m$),\backslash$mu $=0\mathrm{.}15.$

Write the equation of motion of the mass. Do not include the effect of friction.

a$.$ Integrate the EOM for $1$ second starting from rest at $\backslash$theta $(0)=(\backslash$pi $)/(2)$ radians.

b$.$ Plot $\backslash$theta $,\backslash$theta $^(),\backslash$theta $^(),$ the normal force, and total energy of the mass versus time. What do

these plots mean physically and does that make sense? If not, why? Be specific.

Write the equation of motion of the mass including the effect of friction, with coefficient of

kinetic friction $\backslash$mu $.$ Typically we let f$\_($f$)=\backslash$mu N$((\backslash$theta $^()))/(|(\backslash$theta $^())|)=\backslash$mu Nsign$(\backslash$theta $^())$ so that friction opposes motion

as the sign of $\backslash$theta $^()$ changes.

a$.$ Integrate the EOM for $1$ second starting from rest at $\backslash$theta $(0)=(\backslash$pi $)/(2)$ radians.

b$.$ Plot $\backslash$theta $,\backslash$theta $^(),\backslash$theta $^(),$ the normal force, and total energy of the mass versus time. What do

these plots mean physically and does that make sense? If not, why? Be specific.

Improve the model so it behaves as you would anticipate the system behaving with friction.

What did you do or change?

a$.$ Integrate the improved EOM for $1$ second starting from rest at $\backslash$theta $(0)=(\backslash$pi $)/(2)$ radians.

b$.$ Plot $\backslash$theta $,\backslash$theta $^(),\backslash$theta $^(),$ the normal force, and total energy of the mass versus time. What do

these plots mean physically and does that make sense? If not, why? Be specific. $4)$ Build an animation, in a single figure window with $3$ subplots, that shows the motion of the $3$ different systems for the $1$ second of simulation time.

Please put your team number as well as your names on your report. Follow the $9-$Step Process, including a thorough check of your results in Step $9.$ Include your analytical work $($hand calculations$)$ in the Live Script, either as an Appendix or in the body of the report. Export your Live Script to a PDF before you submit it to Canvas.