In Problems 8 through 10 the indicated mass-and-spring system is set in motion from rest (x'₁ (0) = x'₂ (0) = 0) in its equilibrium position (x₁(0) = x₂(0) = 0) with the given external forces F₁(t) and F₂(t) acting on the masses m₁ and m₂, respectively. Find the resulting motion of the system and describe it as a superposition of oscillations at three different frequencies.

The mass-and-spring system of Problem 3, with F₁(t) Ξ 0, F₂(t) = 120 cos 3t

Problem 3

m₁ = 1 , m₂ = 2; k₁ = 1, k₂ = k₃ = 2