To solve the two unknowns, we need another equation. In steady state, the power lost per cycle is equal to the power gained per cycle: ⟨ ⟨ x ˙ ˙ γ γ x ˙ ˙ ⟩ ⟩ ⏟ ⏟ power dissipated = ⟨ ⟨ x ˙ ˙ F cos ⁡ ⁡ ω ω t ⟩ ⟩ ⏟ ⏟ power input , which simplifies to sin ⁡ ⁡ φ φ = − − γ γ X ω ω F .