Maple 9 Learning Guide - Maplesoft

244 • Chapter 7: Solving Calculus ProblemsSimilarly 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 );{x 2 (t) = 1 2 (−2 α m + t2 k + t 2 k α − 2 t k − 2 t k α + k + α k√%1 (t − 1)/+ 2 α cosh() m)Heaviside(t − 1) (kα m√%1 tα (−1 + cosh((1 + α) 2 m) − 2α m )), x 1 (t) = 1 1 + α2 (2 m√%1 (t − 1)− 2 cosh() m + t 2 k + t 2 k α − 2 t k − 2 t k αα m/+ k + α k)Heaviside(t − 1) (k m (1 + α) 2 ) + (√e (− %1 tα m− 2 α cosh() + e (− √%1 tα m) α + e ( √%1 tα m√%1 tα m ))/(1 + α) }%1 := −α m k (1 + α)√ ) + e ( %1 tα m ) α + 2 α