Topic: Theory of Machines / Vibrations
With symbols having the usual meanings, the single degree freedom of system, $m\ddot{x}+c\dot{x}+kx=F \sin\omega t$ represents
- A. Free vibrations with damping
- B. Free vibrations without damping
- C. Forced vibrations with damping
- D. Forced vibrations without damping
Answer: C. Forced vibrations with damping
Explanation: The given differential equation $m\ddot{x}+c\dot{x}+kx=F \sin\omega t$ contains a damping term '$c\dot{x}$' indicating it is a damped system, and an external harmonic excitation force term '$F \sin\omega t$' indicating it is a forced system. Thus, it represents forced vibrations with damping.