Theory of Machine
A single degree of freedom system is given by, m × (d²x/dt²) + c × (dx/dt) + sx = F.cosω.t with usual notations. It represents

Free vibration without damping
Forced vibration with damping
Forced vibration without damping
Free vibration with damping

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Theory of Machine
A system of masses rotating in different parallel planes is in dynamic balance if the

Resultant force and resultant couple are both equal to zero
Resultant force is equal to zero
Resultant force is numerically equal to the resultant couple, but neither of them need necessarily be zero
Resultant couple is equal to zero

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