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For my Physics coursework I'm trying to show how the equation to describe simple harmonic motion, this is where I'm up to now:

http://img408.imageshack.us/img408/4153/untitled8ph.jpg [Broken]

x displacement;

t is time;

k is spring constant;

m is mass.

A is an unknown constant;

b is an unknown constant.

Could somebody check through my working, see if I've gone wrong and hopefully point me in the right direction as to what to do (I've tried respresting the function of e in terms of trigonometric functions but this never made sense.)

Thanks,

Tom

PS. I know it's possible, from the differential equation given, to solve it straight off using the method by assuming it's a quadratic (or something similar) but I want this proof to be rigourous and therefore everything (to some degree) must be explained by me.

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# Homework Help: Struggling with a second-order differential equation

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