(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! d-F dt2 dF dt and di dF dt dt capaCITOR In these equations: t (time) is measured in seconds i (temporal reluctance) is measured in amps F (time warp flux) is measured in jigawatts dF (time warp flux rate) is measured in jigowatts/second dt (time warp acceleration) is measured in jigawatts/per second squared dt 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 i (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! d-F dt2 dF dt and di dF dt dt capaCITOR In these equations: t (time) is measured in seconds i (temporal reluctance) is measured in amps F (time warp flux) is measured in jigawatts dF (time warp flux rate) is measured in jigowatts/second dt (time warp acceleration) is measured in jigawatts/per second squared dt 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 i (temporal reluctance) as a function of time. Be sure to use meaningful plot labels