Forced vibration theory is a concept in physics and engineering that describes the behavior of a system subjected to an external force or input. It is used to analyze and predict the displacement, velocity, and acceleration of a vibrating system under the influence of a driving force.
Forced vibration is different from free vibration in that a free vibration occurs when a system is set into motion and then left to vibrate on its own without any external forces acting upon it. On the other hand, forced vibration is when a system is subjected to an external force or input that causes it to vibrate.
The key components of forced vibration theory include the driving force, the natural frequency of the system, and the damping ratio. The driving force is the external force or input that causes the system to vibrate, the natural frequency is the inherent frequency of the system, and the damping ratio is a measure of the system's energy dissipation.
The solutions for displacement in forced vibration theory can be derived using mathematical equations and principles, such as the equations of motion, Newton's second law, and the principles of energy conservation. These solutions can then be used to predict the amplitude, frequency, and phase of the system's vibration.
Forced vibration theory has many practical applications in various fields, including aerospace engineering, mechanical engineering, and structural engineering. It is used to design and analyze structures and systems that are subjected to external forces, such as bridges, buildings, and aircraft. It is also used in the development of vibration isolation systems and vibration control techniques.