(30 points) The following pair of differential equations describe the behavior of the FLUX Capacitor used in a highly customized DeLorean automobile. IMPORTANT- you may or may not understand the physics of a FLUX Capacitor, but that doesn't matter. The differential equations are given, and you should be able to put them into Matlab can solve them! 1. 2 d F dF dt2 dt di dt dF dt CapaCITOR In these equations: t (time) is measured in seconds l (temporal reluctance) is measured in amps F (time warp flux) is measured in jigawatts dF (time warp flux rate) is measured in jigawatts/second dt d2 F dt2 (time warp acceleration) is measured in jigawatts/per second squared With the following values for the constant parameters: 1=20, k=300, mjf = 5, L=0.1, R=0.5, c=50, and v=12 NOTE: All units for the variables and the constants are consistent as given, and no unit conversions of any kind are necessary. Required a) All initial conditions have a value of zero. Run the simulation for Use Matlab to solve the equations. 3 seconds b) Plot F (time warp flux) as a function of time. Be sure to use meaningful plot labels c) On a separate graph, plot l (temporal reluctance) as a function of time. Be sure to use meaningful plot labels (30 points) The following pair of differential equations describe the behavior of the FLUX Capacitor used in a highly customized DeLorean automobile. IMPORTANT- you may or may not understand the physics of a FLUX Capacitor, but that doesn't matter. The differential equations are given, and you should be able to put them into Matlab can solve them! 1. 2 d F dF dt2 dt di dt dF dt CapaCITOR In these equations: t (time) is measured in seconds l (temporal reluctance) is measured in amps F (time warp flux) is measured in jigawatts dF (time warp flux rate) is measured in jigawatts/second dt d2 F dt2 (time warp acceleration) is measured in jigawatts/per second squared With the following values for the constant parameters: 1=20, k=300, mjf = 5, L=0.1, R=0.5, c=50, and v=12 NOTE: All units for the variables and the constants are consistent as given, and no unit conversions of any kind are necessary. Required a) All initial conditions have a value of zero. Run the simulation for Use Matlab to solve the equations. 3 seconds b) Plot F (time warp flux) as a function of time. Be sure to use meaningful plot labels c) On a separate graph, plot l (temporal reluctance) as a function of time. Be sure to use meaningful plot labels