# * *Damped Harmonic Motion (Differential Equations)

*URGENT*Damped Harmonic Motion (Differential Equations)

A damped harmonic oscillator satisfies the following equation: d2x/dt2 = − 5x − 2dx/dt

(a) By assuming a trial function of the form x = A e^qt, determine the solution of this
equation "from scratch." Express your final answer as a real function, that is, there
should be no i’s in your final answer (where i = (−1)^½).

(b) Your solution to part (a) should have two constants (of integration).
If at t = 0, x = 0.0100 m and dx/dt = 0, determine the numerical values of these two
constants, correct to 3 significant digits.

I have no idea how to do this question. Could somebody(if they can) show me the solution? I have a midterm tomorrow and these are the types of questions I will need answer. I missed this class so I'm completely lost :S

## Answers and Replies

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BruceW
Homework Helper

You should really keep to the physics forums rules and show your own attempt. If you missed the class on complex numbers, then you might not be able to do this question, because q must be a complex number.