I need to model a non linear simple pendulum with air friction.I need help in solving the equations of motion. So, what is the solution for the period θ(t) of a non linear pendulum considering air friction (when sin θ not equal to θ)θ(t) = __________________?Update:θ(t) = a₁cos(ωt + δ) + a₃cos(3ωt + δ) + a₅cos(5ωt + δ) + .... (without damping)θ(t) = e^(-λt)[a₁cos(ωt + δ) + a₃cos(3ωt + δ) + a₅cos(5ωt + δ) + .... (with damping)Please give me the terms for a₁, a₃, a₅, λ and δ. Created by Rs. science-mathematics-en - physics-en

For an undamped (no friction) pendulum, where θ is large (so acceleration is nonlinear with respect to displacement):θ(t) = a₁cos(ωt + δ) + a₃cos(3ωt + δ) + a₅cos(5ωt + δ) + ....See equation 1.5 in the link (a pdf document)To account for damping, multiply the above expression by e^(-λt) where λ is the decay constant of the damping. This gives:θ(t) = e^(-λt)[a₁cos(ωt + δ) + a₃cos(3ωt + δ) + a₅cos(5ωt + δ) + ....]