Total vibration of a harmonically excited system

Equation of motion for harmonically excited system with one degree of freedom

u (t) = \underset{⏟}{e^{- {ζω}_{n} t} (A \cdot \cos (ω_{D} t + B) \cdot \sin (ω_{D} t))} + \underset{⏟}{(C \cdot \sin (ωt) + D \cdot \cos (ωt))}

transient steady - state

t	Time
ω	Angular frequency of excitation
ω_D	Angular frequency
ζ	Damping
A	Constant
B	Constant
C	Constant
D	Constant

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