Question

1.7-1 For the systems described by the equations below, with the input f(t) and output v(t), determine which of the systems are linear and which are nonlinear. dy dt (a) + 2y(t)-f(t) (b) +3y() -se) (e) ( ) +2y(t)-f(t) (d) +92(t) = f(t) (c) 3y(t) + 2 = f(t) (f) + (sin t)y(t)-2 + 2/(t) dt dt (h) v(t)f(r)dr dt

Answer 1

Given Different systems We have to check we then loner or not, (1) Given system is linear if and only if the system satis for super position/(or) linearity theorem. This can found by. T [a_1 x_1 (t) + a_2 x_2 (t)] = a_1 T [x_1 (t)] + a_2 T [x_2 (t)] 1. System differential equation, with non linear functions like square, root, sin, cos, - i e., Ex: sin (x (t)) (or) squareroot x (t) (or) x (t) middot d 2 (t)/dt)^2, d x^2 (t)/dt, tan (y (t) is Non - linear 2. System with initial conditions (or) constant terms is Non - linear Ex dy (t)/dt + 5 y (t) + 5 = x (t) Non linear.(a) dy/dt + 2 y (t) = f^2 (t) Non - linear function Non linear system (b) dy/dt + 3t y (t) = t^2 + (t) Not non linear Hence linear system (e) 3y (t) + 2 = f (t) constant Non - linear (d) (dy/dt)^2 + 2 y (t)