Which of the following options defines a false position on the damping constant "b" present in an oscillatory system and why? (a) a very large constant "b" can prevent a system from oscillating (amplitude 0).
(b) a large constant "b" can prevent a system from being destroyed when it resonates.
(c) a lower constant "b" the oscillation movement decreases its amplitude in a shorter time.
(d) a very large constant "b" makes possible a small oscillation time stopping the system.
(e) the constant "b" depends on the shape of the object and its cross-sectional area.

c) is the right answer, since it is the only FALSE statement among the other 4 options, which are TRUE.

Explanation:

Constant "b" stands for the damping term in the oscillatorry equation, which means it is multiplying the first derivate of the movement variable, be it x (distance) or φ (for angular approaches).

Let's exclude the TRUE options:

a) and d): A very large constant "b" means a high friction into the system, so, if "b" is large enough, it would prevent the system from oscillating (that is, from starting the movement) or, once moving, it may brake it down to zero amplitude within a finite time.b) Indeed, a large enough "b" value would mean a supercritical damping case, in which no oscilation takes place. The system breaks despite the real resonance values in frecuency. This means that only for damping below critical values, resonance may occur.e) Certainly, the friction may be between two solid bodies. In the case a solid body is inside a fluid environment (liquid or gas), "b" value is proportional to the hidrodynamic or aerodinamic resistance, respectively. This "resistance" depends, amongst other variables, on the shape (fluid distribution) and its cross-sectional area (the wider, the more resistance, the greater "b" shall be).

Finally, as exposed above, a greater "b" value involves a a higher damping, then a higher force against the movement, thus shorter times and quicker damping. This is why opcion c) is the FALSE answer, thus the correct option: it states a wrong principle, opposite to the physics.

Hope that was clear enough!  Always think how to exclude answers first, and try to find any option that may be incoherent respect to other(s).

Regards!

A.

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