MATLAB: Numerical simulation of the dynamics of a cylindrical piston entering a coil. Various forces act such as gravity, the force of a spring, and the electrical force. Three different sources are

MATLAB:Numerical simulation of the dynamics of a cylindrical piston entering a coil. Various forces act such as gravity, the force of a spring, and the electrical force. Three different sources are also used to drive the piston.In the attached figure there is an electromagnet with a piston. The circular coil have N = 1000 turns, its resistance is 5Ω and it is fed with an alternating voltage source that can be of three different types:Determine the path x(t), the velocity u(t), the current i(t) through the coil, the electric force on the cylinder Fe(t) and the electromotive force e(t) induced on the coil. Use some program and plot against time for each of the indicated variables.