solving ordinary differential equations vided the signum function sign xis defined to be zero for (numpy sign has this propertyto check that the signs in the definition of are rightrecall that the actual physical force is and this is positive ( when it works against the body moving with velocity the nonlinear spring force is taken as ud tanh , /which is approximately ku for small ubut stabilizes at =for large , here is plot with and oe : : for three valuesif there is no external excitation force acting on the bodywe have the equation of motion mu mg sign tanh ,ud let us simulate situation where body of mass kg slides on surface with : while attached to spring with stiffness kg= the initial displacement of the body is cmand the parameter in uis set to / using the eulercromer function from the osc_ec_general codewe can write function sliding_friction for solving this problemdef sliding_friction()from numpy import tanhsign lambda vmu* * *sign(valpha lambda uk/alpha*tanh(alpha*uf lambda mu