The correct answer is option 'C' - Damping factor.

Explanation:
Damping is a term used to describe the dissipation of energy in a vibrating system. It is important in mechanical engineering as it determines the behavior and stability of a system under dynamic loading. In the context of damping, the ratio of the actual damping coefficient to the critical damping coefficient is referred to as the damping factor.

1. Damping:
Damping refers to the process of reducing or dissipating the energy of oscillations or vibrations in a system. It is achieved by introducing resistance or frictional forces that oppose the motion of the system. Damping is necessary to prevent excessive oscillations, reduce vibration amplitudes, and ensure stability in mechanical systems.

2. Critical Damping:
Critical damping is a specific type of damping in which the system returns to its equilibrium position as quickly as possible without any oscillations. It is the minimum amount of damping required to prevent oscillations in an underdamped system. Critical damping provides the fastest response to an input without overshooting or oscillating about the equilibrium position.

3. Damping Coefficient:
The damping coefficient is a measure of the amount of damping present in a system. It quantifies the resistance to motion and is typically represented by the symbol 'c'. A higher damping coefficient indicates greater resistance to motion and results in a faster decay of oscillations.

4. Damping Factor:
The damping factor is defined as the ratio of the actual damping coefficient to the critical damping coefficient. It is denoted by the symbol 'ζ' (pronounced zeta) and is a dimensionless quantity. The damping factor provides information about the relative amount of damping present in a system compared to the critical damping.

5. Magnification Factor:
The magnification factor is not the correct term for the ratio of the actual damping coefficient to the critical damping coefficient. It refers to the amplification or attenuation of an input signal in a dynamic system. The magnification factor depends on the natural frequency of the system and is used to calculate the response amplitude in the frequency domain.

6. Logarithmic Decrement:
The logarithmic decrement is a measure of the rate at which the amplitude of oscillations decreases over time in a damped system. It is calculated as the natural logarithm of the ratio of any two successive amplitudes. The logarithmic decrement is used to determine the damping ratio and characterize the level of damping in a system.

In conclusion, the correct term for the ratio of the actual damping coefficient to the critical damping coefficient is the damping factor. It is a dimensionless quantity that provides information about the relative amount of damping present in a system compared to the critical damping.