The deviation )t(g of a patient’s blood glucose concentration from its optimal concentration satisfies the differential equation

for α being a positive constant, immediately after the patient fully absorbs a large amount of glucose. The time t is measured in minutes. Identify the type (over-damped, under-damped or critically-damped) of this differential equation. Find the condition on α for which the patient is normal.

The given differential equation is a second-order linear homogeneous ordinary differential equation (ODE) with constant coefficients. It can be written in the standard form:

\[ \frac{d^2g}{dt^2} + \alpha \frac{dg}{dt} + \alpha^2 g = 0 \]

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