Is the system represented by the different equation below, underdamped, overdamp

Question

Is the system represented by the different equation below, underdamped, overdamped, or critically damped? Show your work. 2d2v/dt2 + 4dv/dt + 12v = 32 What is the characteristic equation for the differential equation that represent the following circuit. Show all work. Suppose a series RLC circuit is arranged such that the step response is critically damped. As the components age assume that the capacitor and inductor remain constant but the resistor's value increases. Will the step response become overdamped, underdamped or ramain unchanged? Justify your answer. Lone answer without explanation will not be counted as correct.

Explanation / Answer

since the circuit is critically damped initially , i.e the damping factor =1
where the damping factor = 0.5R((C/L)0.5), as with time the value of R increases , damping factor becomes greater than 1 , the system gets over damped ...

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