Consider the second order differential equation d2/dt^2 x + 6 dx/dt + 10x = 0. Classify the harmonic oscillator
(undamped, underdamped, critically damped, over damped). Justify your answer.
All we need to do is find the auxiliary equation for the given differential equation and solve it like a normal quadratic equation. That is the auxiliary equation needs to be solved by either splitting the middle term or by the quadratic formula that is .
If , then the case will be of under damped oscillation. If the case if of over damped oscillation and if it is critically damped oscillation.
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