Sun28November0333PM 14

The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation.

In which type of sine wave damping does equilibrium at zero amplitude (without overshoot) occur most quickly?

(Please select 1 option)

Overdamping

Critical damping This is the correct answer

Underdamping

Undamped

Optimal damping Incorrect answer selected

Explanation

Critical damping provides the quickest approach to zero amplitude (damping factor = 1).

With overdamping the approach to zero is slower (damping factor >1). Neither sine wave overshoots the zero point.

One example of an oscillatory system is a mass suspended by a spring. When the mass is pulled down and released it bounces up and down. At each bounce the mass is trying to reach its equilibrium point (at zero amplitude) but overshoots by successively decreasing increments until the zero position is reached. The damping ratio is a measure of how rapidly the oscillations decay from one bounce to the next.

In an "undamped" system the mass would bounce indefinitely with each successive oscillation equal to the next. This is purely hypothetical because in practice energy is dissipated and the oscillations will slowly die towards zero. This is an "underdamped" system. (The damping factor <0.7).

With an optimally damped system there is a rapid initial decline in the oscillation to zero amplitude but there is then a small overshoot of about 6-7% of the original amplitude. An optimal damping factor of 0.64 is applied to blood pressure monitoring systems.

Answer Statistics

1

18%

2

34%

3

4%

4

3%

5

43%

Times answered: 241