Learning Guide Learning Guide

6.2 Ordinary Differential Equations • 235eqn1 := α m ( d2dt 2 x 1(t)) = k (x 2 (t) − x 1 (t)) + u(t)Similarly for the second weight.> eqn2 := m*diff(x[2](t),t$2) = k*(x[1](t) - x[2](t));eqn2 := m ( d2dt 2 x 2(t)) = k (x 1 (t) − x 2 (t))Apply a unit step force to the first weight at t = 1.> u := t -> Heaviside(t-1);u := t → Heaviside(t − 1)At time t = 0, both masses are at rest at their respective locations.> ini := x[1](0) = 2, D(x[1])(0) = 0,> x[2](0) = 0, D(x[2])(0) = 0 ;ini := x 1 (0) = 2, D(x 1 )(0) = 0, x 2 (0) = 0, D(x 2 )(0) = 0Solve the problem using Laplace transform methods.> dsolve( {eqn1, eqn2, ini}, {x[1](t), x[2](t)},> method=laplace );