Final answer:
The response of a system with real and unequal roots of its motion equation is considered to be over damped. An overdamped system does not oscillate and reaches equilibrium slowly, as opposed to an underdamped system which oscillates, or a critically damped system which returns to equilibrium the fastest without oscillation. Option C is correct.
Step-by-step explanation:
If the roots of an equation representing the behavior of a system are real and unequal, the system's response is described as over damped. An overdamped system moves toward equilibrium more slowly and doesn’t oscillate about the equilibrium point, unlike an underdamped system, which oscillates and returns to equilibrium quickly.
The critical damping condition is the threshold at which the system returns to equilibrium as quickly as possible without any oscillations. These conditions are especially relevant to the study of a damped mass-spring system or an RLC circuit, where the damping factor is determined by physical properties like resistance, mass, spring constant, and capacitance.
An underdamped system is characterized by having a small damping constant, which results in oscillations that decrease in amplitude over time. On the other hand, critical damping occurs when the damping constant is set at a precise value that allows the system to reach equilibrium swiftly without any oscillations.
The overdamped system, where the system approaches equilibrium very slowly and with no oscillations, occurs when the damping constant is larger than that for critical damping.