Question

differential equation of force oscillation and its solution​

Answer 1

mdt2d2x+bdtdx+kx=F0cosωt⟹dt2d2x+2βdtdx+ω02x=AcosωtThe expected solution is of form x=Dcos(ωt−δ)Put this is in above equation gives,tanδ=ω02−ω22βωFor resonant oscillation, ω0=ω⟹δ=π/2 which is the phase difference between x and F.