Question

Consider the second order differential equation d2/dt^2 x + 6 dx/dt + 10x = 0. Classify...

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.

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Answer #1

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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