Understanding Damped Vibration and Amplitude Reduction

When a body vibrates, it often loses energy due to various factors like air resistance or internal friction. This energy loss causes the amplitude of the vibration to decrease over time. The question describes a situation where the amplitude reduces over every cycle of vibration.

Types of Vibration

Let's look at different types of vibration to understand which one fits this description:

• Free Vibration: This occurs when a body vibrates after an initial disturbance, with no external force acting on it afterwards. Ideally, without energy loss, the amplitude would remain constant. However, in reality, some damping is always present, causing the amplitude to slowly decrease. But the primary characteristic is the absence of a continuous external driving force.
• Forced Vibration: This happens when a body is subjected to a continuous external periodic force. The body vibrates at the frequency of the external force. If there is no damping, the amplitude can become very large, especially near resonance. With damping, the amplitude reaches a steady state determined by the driving force, frequency, and damping level.
• Damped Vibration: This specifically refers to vibration where energy is dissipated from the vibrating system. This dissipation causes the amplitude of the vibration to gradually decrease with each cycle until the vibration stops. Damping forces, like friction or air resistance, are responsible for this reduction in amplitude.

Why Amplitude Reduces in Damped Vibration

In damped vibration, a damping force (like air resistance or friction) opposes the motion of the vibrating object. This damping force does work against the motion, converting the system's mechanical energy into other forms, such as heat. As energy is lost, the total energy of the vibration decreases, leading to a reduction in the maximum displacement from the equilibrium position, which is the amplitude.

The rate at which the amplitude reduces depends on the amount of damping present in the system. In light damping, the amplitude decays slowly over many cycles. In heavy damping, it decays quickly, and in critical damping or overdamping, the oscillation might not even complete a full cycle before returning to equilibrium.

Conclusion

The question states that there is a reduction in amplitude over every cycle of vibration. This phenomenon is the defining characteristic of damped vibration.