The Euler method treats Newton's second law (N2) as a set of "marching orders." Given the "state of an object (its position and velocity) at a particular time, t, it uses N2 to calculate (predict) the state of the object (its position and velocity) at a later time, t + Δt.

(a) For a cart on a spring, taking the coordinate to start at 0 at the equilibrium position, write N2 for the cart.

(b) Rewrite N2 for the time interval from t to t + Δt and show how to rewrite this form to give Euler's method -- a way of calculating the position and velocity at a time t + Δt given the position and velocity at a time t.