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 7, with F₁(t) = 30 cost, F₂(t) = 60 cost

Problem 7

m₁ = m₂ = 1; k₁ = 4, k₂ = 6, k₃ = 4