Applying the virial theorem, we have m ⟨ ⟨ x ˙ ˙ x ˙ ˙ ⟩ ⟩ = k ⟨ ⟨ x x ⟩ ⟩ + γ γ ⟨ ⟨ x x ˙ ˙ ⟩ ⟩ − − F ⟨ ⟨ cos ⁡ ⁡ ( ω ω t ) x ⟩ ⟩ , which simplifies to F cos ⁡ ⁡ ( φ φ ) = m ( ω ω 0 2 − − ω ω 2 ) X , where ω ω 0 = k / m is the natural frequency of the oscillator.