Question

If the damping factor of the vibrating system is considered as unity, then the type of system is said to be

• A. over damped
• B. critically damped
• C. under damped
• D. un-damped

Hint:

Remember the critical values for the damping ratio \( \zeta \): - \( \zeta<1 \): Underdamped (oscillates) - \( \zeta = 1 \): Critically damped (returns to equilibrium fastest without oscillation) - \( \zeta>1 \): Overdamped (returns to equilibrium slowly without oscillation) - \( \zeta = 0 \): Undamped (oscillates indefinitely) This classification is fundamental in understanding the dynamic behavior of vibrating systems.

Answer 1

The Correct Option is B

Step 1: Understand the concept of damping factor in vibrating systems.
In the study of vibrations, the damping factor (also known as the damping ratio, denoted by \( \zeta \)) is a dimensionless measure describing how oscillations in a system decay after a disturbance. It is a critical parameter that determines the type of damping a system experiences.
Step 2: Relate damping factor to different types of damping. There are typically three main types of damping for a single-degree-of-freedom vibrating system, categorized by the value of the damping factor \( \zeta \):
Underdamped System (\( \zeta<1 \)): In an underdamped system, the damping is light, and the system oscillates with decreasing amplitude before eventually settling down. It completes at least one oscillation.
Critically Damped System (\( \zeta = 1 \)): A critically damped system returns to its equilibrium position as quickly as possible without oscillating. This condition represents the boundary between underdamped and overdamped behavior. The system dissipates energy as fast as possible without overshoot.
Overdamped System (\( \zeta>1 \)): In an overdamped system, the damping is so strong that the system returns to equilibrium without oscillating, but it does so more slowly than a critically damped system. There is no overshoot.
Undamped System (\( \zeta = 0 \)): An undamped system has no energy dissipation, and it oscillates indefinitely at its natural frequency once disturbed.
Step 3: Apply the given condition to identify the system type. The problem states that "the damping factor of the vibrating system is considered as unity". Unity means a value of 1. So, we have \( \zeta = 1 \). According to the definitions in Step 2, a system with a damping factor of unity (\( \zeta = 1 \)) is defined as a critically damped system. The final answer is \( \boxed{\text{critically damped}} \).